Hilbert's \(19^{\text{th}}\) problem revisited

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 conc...

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Bibliographic Details
Published in:arXiv.org 2022-01
Main Author: Mooney, Connor
Format: Article
Language:English
Subjects:
Regularity
Online Access:Get full text
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Summary: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.
ISSN:2331-8422