Hilbert's $19^{\text{th}}$ problem revisited Article Swipe
In this survey article we revisit Hilbert's $19^{\text{th}}$ problem concerning the regularity of minimizers of variational integrals. We first discuss the classical theory (that is, the statement and resolution of Hilbert's problem in all dimensions). We then discuss recent results concerning the regularity of minimizers of degenerate convex functionals. Finally, we discuss some open problems. Exercises are included for the benefit of researchers who are entering the subject.
Related Topics
Concepts
Statement (logic)
Degenerate energy levels
Regular polygon
Resolution (logic)
Mathematics
Subject (documents)
Problem statement
Hilbert space
Pure mathematics
Computer science
Linguistics
Artificial intelligence
Philosophy
Physics
Quantum mechanics
Management science
Geometry
Library science
Economics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2106.02507
- https://arxiv.org/pdf/2106.02507
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4287125235
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4287125235Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2106.02507Digital Object Identifier
- Title
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Hilbert's $19^{\text{th}}$ problem revisitedWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-06-04Full publication date if available
- Authors
-
Connor MooneyList of authors in order
- Landing page
-
https://arxiv.org/abs/2106.02507Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2106.02507Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2106.02507Direct OA link when available
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Statement (logic), Degenerate energy levels, Regular polygon, Resolution (logic), Mathematics, Subject (documents), Problem statement, Hilbert space, Pure mathematics, Computer science, Linguistics, Artificial intelligence, Philosophy, Physics, Quantum mechanics, Management science, Geometry, Library science, EconomicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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