Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local H\"older and maximal regularity of solutions of elliptic equations
  with superquadratic gradient terms   We study the local H\"older regularity of strong solutions $u$ of
second-order uniformly elliptic equations having a gradient term with
superquadratic growth $\gamma > 2$, and right-hand side in a Lebesgue space
$L^q$. When $q > N\frac{\gamma-1}{\gamma}$ ($N$ is the dimension of the
Euclidean space), we obtain the optimal H\"older continuity exponent $\alpha_q
> \frac{\gamma-2}{\gamma-1}$. This allows us to prove some new results of
maximal regularity type, which consist in estimating the Hessian matrix of $u$
in $L^q$. Our methods are based on blow-up techniques and a Liouville theorem.

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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph