Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimizers of convex functionals with small degeneracy set   We study the question whether Lipschitz minimizers of $\int F(\nabla u)\,dx$
in $\mathbb{R}^n$ are $C^1$ when $F$ is strictly convex. Building on work of De
Silva-Savin, we confirm the $C^1$ regularity when $D^2F$ is positive and
bounded away from finitely many points that lie in a $2$-plane. We then
construct a counterexample in $\mathbb{R}^4$, where $F$ is strictly convex but
$D^2F$ degenerates on the intersection of a Simons cone with $S^3$. Finally we
highlight a connection between the case $n = 3$ and a result of Alexandrov in
classical differential geometry, and we make a conjecture about this case.

16
The categories of this paper are: stat
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex