Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of stable solutions to reaction-diffusion elliptic equations   The boundedness of stable solutions to semilinear (or reaction-diffusion)
elliptic PDEs has been studied since the 1970's. In dimensions 10 and higher,
there exist stable energy solutions which are unbounded (or singular). This
note describes, for non-expert readers, a recent work in collaboration with
Figalli, Ros-Oton, and Serra, where we prove that stable solutions are smooth
up to the optimal dimension 9. This answers to an open problem posed by Brezis
in the mid-nineties concerning the regularity of extremal solutions to
Gelfand-type problems.
  We also describe, briefly, a famous analogue question in differential
geometry: the regularity of stable minimal surfaces.

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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas