Hilbert's $19^{\text{th}}$ problem revisited
Analysis of PDEs
2022-01-05 v2
Abstract
In this survey article we revisit Hilbert's 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.
Keywords
Cite
@article{arxiv.2106.02507,
title = {Hilbert's $19^{\text{th}}$ problem revisited},
author = {Connor Mooney},
journal= {arXiv preprint arXiv:2106.02507},
year = {2022}
}
Comments
25 pages, to appear in Boll. Unione Mat. Ital