Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffusion with nonlocal Dirichlet boundary conditions on unbounded
  domains   We consider a second order differential operator $\mathscr{A}$ on an
(typically unbounded) open and Dirichlet regular set $\Omega\subset
\mathbb{R}^d$ and subject to nonlocal Dirichlet boundary conditions of the form
\[ u(z) = \int_\Omega u(x)\mu (z, dx) \quad \mbox{ for } z\in \partial \Omega.
\] Here, $\mu : \partial\Omega \to \mathscr{M}(\Omega)$ is a $\sigma
(\mathscr{M}(\Omega), C_b(\Omega))$-continuous map taking values in the
probability measures on $\Omega$. Under suitable assumptions on the
coefficients in $\mathscr{A}$, which may be unbounded, we prove that a
realization $A_\mu$ of $\mathscr{A}$ subject to the nonlocal boundary
condition, generates a (not strongly continuous) semigroup on
$L^\infty(\Omega)$. We also establish a sufficient condition for this semigroup
to be Markovian and prove that in this case, it enjoys the strong Feller
property. We also study the asymptotic behavior of the semigroup.

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The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
14
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: hep-ex
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int