Hilbert's 19th problem revisited Article Swipe
In these notes we revisit Hilbert's 19th 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. To conclude we discuss some open problems. The notes are based on a lecture series given by the author for the workshop Summer Program in PDEs organized by UT Austin (and conducted online) in May 2021.
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Concepts
Statement (logic)
Degenerate energy levels
Regular polygon
Series (stratigraphy)
Mathematics
Resolution (logic)
Calculus (dental)
Pure mathematics
Applied mathematics
Computer science
Epistemology
Philosophy
Physics
Artificial intelligence
Quantum mechanics
Geometry
Biology
Dentistry
Paleontology
Medicine
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://arxiv.org/pdf/2106.02507
- OA Status
- green
- Cited By
- 1
- References
- 27
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W3171484933
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Hilbert's 19th problem revisitedWork title
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2021Year of publication
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2021-06-04Full publication date if available
- Authors
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Connor MooneyList of authors in order
- Landing page
-
https://arxiv.org/pdf/2106.02507Publisher landing page
- Open access
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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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, Series (stratigraphy), Mathematics, Resolution (logic), Calculus (dental), Pure mathematics, Applied mathematics, Computer science, Epistemology, Philosophy, Physics, Artificial intelligence, Quantum mechanics, Geometry, Biology, Dentistry, Paleontology, MedicineTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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27Number of works referenced by this work
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20Other works algorithmically related by OpenAlex
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