Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Liouville type theorems and regularity of solutions to degenerate or
  singular problems part II: odd solutions   We consider a class of equations in divergence form with a
singular/degenerate weight $$ -\mathrm{div}(|y|^a A(x,y)\nabla u)=|y|^a
f(x,y)+\textrm{div}(|y|^aF(x,y))\;. $$ Under suitable regularity assumptions
for the matrix $A$, the forcing term $f$ and the field $F$, we prove H\"older
continuity of solutions which are odd in $y\in\mathbb{R}$, and possibly of
their derivatives. In addition, we show stability of the $C^{0,\alpha}$ and
$C^{1,\alpha}$ a priori bounds for approximating problems in the form $$
-\mathrm{div}((\varepsilon^2+y^2)^{a/2} A(x,y)\nabla
u)=(\varepsilon^2+y^2)^{a/2}
f(x,y)+\textrm{div}((\varepsilon^2+y^2)^{a/2}F(x,y)) $$ as $\varepsilon\to 0$.
Our method is based upon blow-up and appropriate Liouville type theorems.

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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg