Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An extension problem for sums of fractional Laplacians and 1-D symmetry
  of phase transitions   We study nonlinear elliptic equations for operators corresponding to
non-stable L\'evy diffusions. We include a sum of fractional Laplacians of
different orders. Such operators are infinitesimal generators of non-stable
(i.e., non self-similar) L\'evy processes. We establish the regularity of
solutions, as well as sharp energy estimates. As a consequence, we prove a 1-D
symmetry result for monotone solutions to Allen-Cahn type equations with a
non-stable L\'evy diffusion. These operators may still be realized as local
operators using a system of PDEs ---in the spirit of the extension problem of
Caffarelli and Silvestre.

18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph