Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional Laplacians in bounded domains: Killed, reflected, censored
  and taboo L\'evy flights   The fractional Laplacian $(- \Delta)^{\alpha /2}$, $\alpha \in (0,2)$ has
many equivalent (albeit formally different) realizations as a nonlocal
generator of a family of $\alpha $-stable stochastic processes in $R^n$. On the
other hand, if the process is to be restricted to a bounded domain, there are
many inequivalent proposals for what a boundary-data respecting fractional
Laplacian should actually be. This ambiguity holds true not only for each
specific choice of the process behavior at the boundary (like e.g. absorbtion,
reflection, conditioning or boundary taboos), but extends as well to its
particular technical implementation (Dirchlet, Neumann, etc. problems). The
inferred jump-type processes are inequivalent as well, differing in their
spectral and statistical characteristics. In the present paper we focus on
L\'evy flight-induced jump-type processes which are constrained to stay forever
inside a finite domain. That refers to a concept of taboo processes (imported
from Brownian to L\'evy - stable contexts), to so-called censored processes and
to reflected L\'evy flights whose status still remains to be settled on both
physical and mathematical grounds. As a byproduct of our fractional spectral
analysis, with reference to Neumann boundary conditions, we discuss disordered
semiconducting heterojunctions as the bounded domain problem.

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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th