Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric regularity for elliptic equations in double-divergence form   In this paper, we examine the regularity of the solutions to the
double-divergence equation. We establish improved H\"older continuity as
solutions approach their zero level-sets. In fact, we prove that
$\alpha$-H\"older continuous coefficients lead to solutions of class
$\mathcal{C}^{1^-}$, locally. Under the assumption of Sobolev differentiable
coefficients, we establish regularity in the class $\mathcal{C}^{1,1^-}$. Our
results unveil improved continuity along a nonphysical free boundary, where the
weak formulation of the problem vanishes. We argue through a geometric set of
techniques, implemented by approximation methods. Such methods connect our
problem of interest with a target profile. An iteration procedure imports
information from this limiting configuration to the solutions of the
double-divergence equation.

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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin