An extrapolation result in the variational setting: improved regularity, compactness, and applications to quasilinear systems Article Swipe
Sebastian Bechtel
,
Mark Veraar
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1007/s40072-025-00378-9
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1007/s40072-025-00378-9
In this paper we consider the variational setting for SPDE on a Gelfand triple $$(V, H, V^*)$$ . Under the standard conditions on a linear coercive pair ( A , B ), and a symmetry condition on A we manage to extrapolate the classical $$\textrm{L}^2$$ -estimates in time to $$\textrm{L}^p$$ -estimates for some $$p>2$$ without any further conditions on ( A , B ). As a consequence we obtain several other a priori regularity results of the paths of the solution. Under the assumption that V embeds compactly into H , we derive a universal compactness result quantifying over all ( A , B ). As an application of the compactness result we prove global existence of weak solutions to a system of second order quasi-linear equations.
Related Topics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1007/s40072-025-00378-9
- https://link.springer.com/content/pdf/10.1007/s40072-025-00378-9.pdf
- OA Status
- hybrid
- Cited By
- 1
- References
- 31
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4412188179
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4412188179Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1007/s40072-025-00378-9Digital Object Identifier
- Title
-
An extrapolation result in the variational setting: improved regularity, compactness, and applications to quasilinear systemsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2025Year of publication
- Publication date
-
2025-07-11Full publication date if available
- Authors
-
Sebastian Bechtel, Mark VeraarList of authors in order
- Landing page
-
https://doi.org/10.1007/s40072-025-00378-9Publisher landing page
- PDF URL
-
https://link.springer.com/content/pdf/10.1007/s40072-025-00378-9.pdfDirect link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
hybridOpen access status per OpenAlex
- OA URL
-
https://link.springer.com/content/pdf/10.1007/s40072-025-00378-9.pdfDirect OA link when available
- Concepts
-
Extrapolation, Compact space, Applied mathematics, Mathematics, Mathematical analysisTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1Per-year citation counts (last 5 years)
- References (count)
-
31Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4412188179 |
|---|---|
| doi | https://doi.org/10.1007/s40072-025-00378-9 |
| ids.doi | https://doi.org/10.1007/s40072-025-00378-9 |
| ids.pmid | https://pubmed.ncbi.nlm.nih.gov/41211044 |
| ids.openalex | https://openalex.org/W4412188179 |
| fwci | 5.01839543 |
| type | article |
| title | An extrapolation result in the variational setting: improved regularity, compactness, and applications to quasilinear systems |
| awards[0].id | https://openalex.org/G1818990546 |
| awards[0].funder_id | https://openalex.org/F4320321800 |
| awards[0].display_name | |
| awards[0].funder_award_id | VI.C.212.027 |
| awards[0].funder_display_name | Nederlandse Organisatie voor Wetenschappelijk Onderzoek |
| biblio.issue | 4 |
| biblio.volume | 13 |
| biblio.last_page | 2038 |
| biblio.first_page | 2000 |
| topics[0].id | https://openalex.org/T12100 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.9998999834060669 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1703 |
| topics[0].subfield.display_name | Computational Theory and Mathematics |
| topics[0].display_name | Advanced Mathematical Modeling in Engineering |
| topics[1].id | https://openalex.org/T11110 |
| topics[1].field.id | https://openalex.org/fields/22 |
| topics[1].field.display_name | Engineering |
| topics[1].score | 0.9995999932289124 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2207 |
| topics[1].subfield.display_name | Control and Systems Engineering |
| topics[1].display_name | Stability and Controllability of Differential Equations |
| topics[2].id | https://openalex.org/T10194 |
| topics[2].field.id | https://openalex.org/fields/26 |
| topics[2].field.display_name | Mathematics |
| topics[2].score | 0.9994999766349792 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2604 |
| topics[2].subfield.display_name | Applied Mathematics |
| topics[2].display_name | Nonlinear Partial Differential Equations |
| funders[0].id | https://openalex.org/F4320308269 |
| funders[0].ror | https://ror.org/012kf4317 |
| funders[0].display_name | Alexander von Humboldt-Stiftung |
| funders[1].id | https://openalex.org/F4320321800 |
| funders[1].ror | https://ror.org/04jsz6e67 |
| funders[1].display_name | Nederlandse Organisatie voor Wetenschappelijk Onderzoek |
| is_xpac | False |
| apc_list.value | 2290 |
| apc_list.currency | EUR |
| apc_list.value_usd | 2890 |
| apc_paid.value | 2290 |
| apc_paid.currency | EUR |
| apc_paid.value_usd | 2890 |
| concepts[0].id | https://openalex.org/C132459708 |
| concepts[0].level | 2 |
| concepts[0].score | 0.9287240505218506 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q744069 |
| concepts[0].display_name | Extrapolation |
| concepts[1].id | https://openalex.org/C18648836 |
| concepts[1].level | 2 |
| concepts[1].score | 0.8772169351577759 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q381892 |
| concepts[1].display_name | Compact space |
| concepts[2].id | https://openalex.org/C28826006 |
| concepts[2].level | 1 |
| concepts[2].score | 0.5197672247886658 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q33521 |
| concepts[2].display_name | Applied mathematics |
| concepts[3].id | https://openalex.org/C33923547 |
| concepts[3].level | 0 |
| concepts[3].score | 0.4683980941772461 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[3].display_name | Mathematics |
| concepts[4].id | https://openalex.org/C134306372 |
| concepts[4].level | 1 |
| concepts[4].score | 0.3781166076660156 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[4].display_name | Mathematical analysis |
| keywords[0].id | https://openalex.org/keywords/extrapolation |
| keywords[0].score | 0.9287240505218506 |
| keywords[0].display_name | Extrapolation |
| keywords[1].id | https://openalex.org/keywords/compact-space |
| keywords[1].score | 0.8772169351577759 |
| keywords[1].display_name | Compact space |
| keywords[2].id | https://openalex.org/keywords/applied-mathematics |
| keywords[2].score | 0.5197672247886658 |
| keywords[2].display_name | Applied mathematics |
| keywords[3].id | https://openalex.org/keywords/mathematics |
| keywords[3].score | 0.4683980941772461 |
| keywords[3].display_name | Mathematics |
| keywords[4].id | https://openalex.org/keywords/mathematical-analysis |
| keywords[4].score | 0.3781166076660156 |
| keywords[4].display_name | Mathematical analysis |
| language | en |
| locations[0].id | doi:10.1007/s40072-025-00378-9 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4210228365 |
| locations[0].source.issn | 2194-0401, 2194-041X |
| locations[0].source.type | journal |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 2194-0401 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Stochastic Partial Differential Equations Analysis and Computations |
| locations[0].source.host_organization | https://openalex.org/P4310319900 |
| locations[0].source.host_organization_name | Springer Science+Business Media |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310319900, https://openalex.org/P4310319965 |
| locations[0].source.host_organization_lineage_names | Springer Science+Business Media, Springer Nature |
| locations[0].license | cc-by |
| locations[0].pdf_url | https://link.springer.com/content/pdf/10.1007/s40072-025-00378-9.pdf |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Stochastics and Partial Differential Equations: Analysis and Computations |
| locations[0].landing_page_url | https://doi.org/10.1007/s40072-025-00378-9 |
| locations[1].id | pmid:41211044 |
| locations[1].is_oa | False |
| locations[1].source.id | https://openalex.org/S4306525036 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | PubMed |
| locations[1].source.host_organization | https://openalex.org/I1299303238 |
| locations[1].source.host_organization_name | National Institutes of Health |
| locations[1].source.host_organization_lineage | https://openalex.org/I1299303238 |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | publishedVersion |
| locations[1].raw_type | |
| locations[1].license_id | |
| locations[1].is_accepted | True |
| locations[1].is_published | True |
| locations[1].raw_source_name | Stochastic partial differential equations : analysis and computations |
| locations[1].landing_page_url | https://pubmed.ncbi.nlm.nih.gov/41211044 |
| locations[2].id | pmh:oai:europepmc.org:11399044 |
| locations[2].is_oa | True |
| locations[2].source.id | https://openalex.org/S4306400806 |
| locations[2].source.issn | |
| locations[2].source.type | repository |
| locations[2].source.is_oa | False |
| locations[2].source.issn_l | |
| locations[2].source.is_core | False |
| locations[2].source.is_in_doaj | False |
| locations[2].source.display_name | Europe PMC (PubMed Central) |
| locations[2].source.host_organization | https://openalex.org/I1303153112 |
| locations[2].source.host_organization_name | European Bioinformatics Institute |
| locations[2].source.host_organization_lineage | https://openalex.org/I1303153112 |
| locations[2].license | other-oa |
| locations[2].pdf_url | |
| locations[2].version | submittedVersion |
| locations[2].raw_type | Text |
| locations[2].license_id | https://openalex.org/licenses/other-oa |
| locations[2].is_accepted | False |
| locations[2].is_published | False |
| locations[2].raw_source_name | |
| locations[2].landing_page_url | https://www.ncbi.nlm.nih.gov/pmc/articles/12589295 |
| indexed_in | crossref, pubmed |
| authorships[0].author.id | https://openalex.org/A5004816364 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-1450-2285 |
| authorships[0].author.display_name | Sebastian Bechtel |
| authorships[0].countries | NL |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I98358874 |
| authorships[0].affiliations[0].raw_affiliation_string | Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands |
| authorships[0].institutions[0].id | https://openalex.org/I98358874 |
| authorships[0].institutions[0].ror | https://ror.org/02e2c7k09 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I98358874 |
| authorships[0].institutions[0].country_code | NL |
| authorships[0].institutions[0].display_name | Delft University of Technology |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Sebastian Bechtel |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands |
| authorships[1].author.id | https://openalex.org/A5083145406 |
| authorships[1].author.orcid | https://orcid.org/0000-0003-3167-7471 |
| authorships[1].author.display_name | Mark Veraar |
| authorships[1].countries | NL |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I98358874 |
| authorships[1].affiliations[0].raw_affiliation_string | Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands |
| authorships[1].institutions[0].id | https://openalex.org/I98358874 |
| authorships[1].institutions[0].ror | https://ror.org/02e2c7k09 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I98358874 |
| authorships[1].institutions[0].country_code | NL |
| authorships[1].institutions[0].display_name | Delft University of Technology |
| authorships[1].author_position | last |
| authorships[1].raw_author_name | Mark Veraar |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands |
| has_content.pdf | True |
| has_content.grobid_xml | True |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://link.springer.com/content/pdf/10.1007/s40072-025-00378-9.pdf |
| open_access.oa_status | hybrid |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | An extrapolation result in the variational setting: improved regularity, compactness, and applications to quasilinear systems |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T23:17:08.748858 |
| primary_topic.id | https://openalex.org/T12100 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.9998999834060669 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1703 |
| primary_topic.subfield.display_name | Computational Theory and Mathematics |
| primary_topic.display_name | Advanced Mathematical Modeling in Engineering |
| related_works | https://openalex.org/W4391375266, https://openalex.org/W1968270095, https://openalex.org/W4296478327, https://openalex.org/W1960072520, https://openalex.org/W2042397106, https://openalex.org/W4361730764, https://openalex.org/W1965029248, https://openalex.org/W2220129715, https://openalex.org/W2387596242, https://openalex.org/W3048095155 |
| cited_by_count | 1 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 1 |
| locations_count | 3 |
| best_oa_location.id | doi:10.1007/s40072-025-00378-9 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4210228365 |
| best_oa_location.source.issn | 2194-0401, 2194-041X |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | False |
| best_oa_location.source.issn_l | 2194-0401 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | Stochastic Partial Differential Equations Analysis and Computations |
| best_oa_location.source.host_organization | https://openalex.org/P4310319900 |
| best_oa_location.source.host_organization_name | Springer Science+Business Media |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310319900, https://openalex.org/P4310319965 |
| best_oa_location.source.host_organization_lineage_names | Springer Science+Business Media, Springer Nature |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | https://link.springer.com/content/pdf/10.1007/s40072-025-00378-9.pdf |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Stochastics and Partial Differential Equations: Analysis and Computations |
| best_oa_location.landing_page_url | https://doi.org/10.1007/s40072-025-00378-9 |
| primary_location.id | doi:10.1007/s40072-025-00378-9 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4210228365 |
| primary_location.source.issn | 2194-0401, 2194-041X |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 2194-0401 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Stochastic Partial Differential Equations Analysis and Computations |
| primary_location.source.host_organization | https://openalex.org/P4310319900 |
| primary_location.source.host_organization_name | Springer Science+Business Media |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310319900, https://openalex.org/P4310319965 |
| primary_location.source.host_organization_lineage_names | Springer Science+Business Media, Springer Nature |
| primary_location.license | cc-by |
| primary_location.pdf_url | https://link.springer.com/content/pdf/10.1007/s40072-025-00378-9.pdf |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Stochastics and Partial Differential Equations: Analysis and Computations |
| primary_location.landing_page_url | https://doi.org/10.1007/s40072-025-00378-9 |
| publication_date | 2025-07-11 |
| publication_year | 2025 |
| referenced_works | https://openalex.org/W2997071108, https://openalex.org/W4391473755, https://openalex.org/W3167603299, https://openalex.org/W4400467187, https://openalex.org/W4300857049, https://openalex.org/W2070189398, https://openalex.org/W4253840677, https://openalex.org/W4390154192, https://openalex.org/W2792839858, https://openalex.org/W1545761024, https://openalex.org/W2002027491, https://openalex.org/W1651267457, https://openalex.org/W1981007600, https://openalex.org/W2963865157, https://openalex.org/W2505236330, https://openalex.org/W4401459654, https://openalex.org/W2564836132, https://openalex.org/W4302577166, https://openalex.org/W4389441988, https://openalex.org/W2495773218, https://openalex.org/W1507925093, https://openalex.org/W2338895534, https://openalex.org/W2946339954, https://openalex.org/W2086649450, https://openalex.org/W2486411918, https://openalex.org/W2963537024, https://openalex.org/W4393122351, https://openalex.org/W4252609867, https://openalex.org/W2149673086, https://openalex.org/W3105683009, https://openalex.org/W3100417407 |
| referenced_works_count | 31 |
| abstract_inverted_index.( | 43, 97, 138 |
| abstract_inverted_index., | 45, 99, 128, 140 |
| abstract_inverted_index.. | 33 |
| abstract_inverted_index.A | 44, 53, 98, 139 |
| abstract_inverted_index.B | 46, 100, 141 |
| abstract_inverted_index.H | 127 |
| abstract_inverted_index.V | 123 |
| abstract_inverted_index.a | 12, 39, 49, 103, 109, 131, 158 |
| abstract_inverted_index.), | 47 |
| abstract_inverted_index.). | 101, 142 |
| abstract_inverted_index.As | 102, 143 |
| abstract_inverted_index.H, | 16 |
| abstract_inverted_index.In | 1 |
| abstract_inverted_index.an | 144 |
| abstract_inverted_index.in | 69 |
| abstract_inverted_index.of | 113, 116, 146, 154, 160 |
| abstract_inverted_index.on | 11, 38, 52, 96 |
| abstract_inverted_index.to | 56, 71, 157 |
| abstract_inverted_index.we | 4, 54, 105, 129, 150 |
| abstract_inverted_index.all | 137 |
| abstract_inverted_index.and | 48 |
| abstract_inverted_index.any | 93 |
| abstract_inverted_index.for | 9, 81 |
| abstract_inverted_index.the | 6, 35, 58, 114, 117, 120, 147 |
| abstract_inverted_index.SPDE | 10 |
| abstract_inverted_index.into | 126 |
| abstract_inverted_index.over | 136 |
| abstract_inverted_index.pair | 42 |
| abstract_inverted_index.some | 82 |
| abstract_inverted_index.that | 122 |
| abstract_inverted_index.this | 2 |
| abstract_inverted_index.time | 70 |
| abstract_inverted_index.weak | 155 |
| abstract_inverted_index.$$(V, | 15 |
| abstract_inverted_index.Under | 34, 119 |
| abstract_inverted_index.order | 162 |
| abstract_inverted_index.other | 108 |
| abstract_inverted_index.paper | 3 |
| abstract_inverted_index.paths | 115 |
| abstract_inverted_index.prove | 151 |
| abstract_inverted_index.V^*)$$ | 17 |
| abstract_inverted_index.derive | 130 |
| abstract_inverted_index.embeds | 124 |
| abstract_inverted_index.global | 152 |
| abstract_inverted_index.linear | 40 |
| abstract_inverted_index.manage | 55 |
| abstract_inverted_index.obtain | 106 |
| abstract_inverted_index.priori | 110 |
| abstract_inverted_index.result | 134, 149 |
| abstract_inverted_index.second | 161 |
| abstract_inverted_index.system | 159 |
| abstract_inverted_index.triple | 14 |
| abstract_inverted_index.Gelfand | 13 |
| abstract_inverted_index.further | 94 |
| abstract_inverted_index.results | 112 |
| abstract_inverted_index.setting | 8 |
| abstract_inverted_index.several | 107 |
| abstract_inverted_index.without | 92 |
| abstract_inverted_index.Abstract | 0 |
| abstract_inverted_index.coercive | 41 |
| abstract_inverted_index.consider | 5 |
| abstract_inverted_index.standard | 36 |
| abstract_inverted_index.symmetry | 50 |
| abstract_inverted_index.<mml:math | 18, 61, 73, 84 |
| abstract_inverted_index.classical | 59 |
| abstract_inverted_index.compactly | 125 |
| abstract_inverted_index.condition | 51 |
| abstract_inverted_index.existence | 153 |
| abstract_inverted_index.solution. | 118 |
| abstract_inverted_index.solutions | 156 |
| abstract_inverted_index.universal | 132 |
| abstract_inverted_index.$$p>2$$ | 83 |
| abstract_inverted_index.-estimates | 68, 80 |
| abstract_inverted_index.<mml:mrow> | 20, 86 |
| abstract_inverted_index.<mml:msup> | 26, 63, 75 |
| abstract_inverted_index.assumption | 121 |
| abstract_inverted_index.conditions | 37, 95 |
| abstract_inverted_index.equations. | 164 |
| abstract_inverted_index.regularity | 111 |
| abstract_inverted_index.</mml:math> | 32, 67, 79, 91 |
| abstract_inverted_index.</mml:mrow> | 31, 90 |
| abstract_inverted_index.</mml:msup> | 29, 66, 78 |
| abstract_inverted_index.application | 145 |
| abstract_inverted_index.compactness | 133, 148 |
| abstract_inverted_index.consequence | 104 |
| abstract_inverted_index.extrapolate | 57 |
| abstract_inverted_index.quantifying | 135 |
| abstract_inverted_index.variational | 7 |
| abstract_inverted_index.quasi-linear | 163 |
| abstract_inverted_index.$$\textrm{L}^2$$ | 60 |
| abstract_inverted_index.$$\textrm{L}^p$$ | 72 |
| abstract_inverted_index.<mml:mi>H</mml:mi> | 24 |
| abstract_inverted_index.<mml:mi>V</mml:mi> | 22, 27 |
| abstract_inverted_index.<mml:mi>p</mml:mi> | 77, 87 |
| abstract_inverted_index.<mml:mn>2</mml:mn> | 65, 89 |
| abstract_inverted_index.<mml:mo>(</mml:mo> | 21 |
| abstract_inverted_index.<mml:mo>)</mml:mo> | 30 |
| abstract_inverted_index.<mml:mo>,</mml:mo> | 23, 25 |
| abstract_inverted_index.<mml:mo>∗</mml:mo> | 28 |
| abstract_inverted_index.<mml:mo>></mml:mo> | 88 |
| abstract_inverted_index.<mml:mtext>L</mml:mtext> | 64, 76 |
| abstract_inverted_index.xmlns:mml="http://www.w3.org/1998/Math/MathML"> | 19, 62, 74, 85 |
| cited_by_percentile_year.max | 95 |
| cited_by_percentile_year.min | 91 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.9067348 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |