Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The unique continuation property of sublinear equations   We derive the unique continuation property of a class of semi-linear elliptic
equations with non-Lipschitz nonlinearities. The simplest type of equations to
which our results apply is given as $-\Delta u = |u|^{\sigma-1} u$ in a domain
$\Omega \subset \mathbb{R}^N$, with $0 \le \sigma <1$. Despite the sublinear
character of the nonlinear term, we prove that if a solution vanishes in an
open subset of $\Omega$, then it vanishes necessarily in the whole $\Omega$. We
then extend the result to equations with variable coefficients operators and
inhomogeneous right-hand side.

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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn