Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intrinsic ultracontractivity of nonsymmetric diffusions with
  measure-valued drifts and potentials   Recently, in [Preprint (2006)], we extended the concept of intrinsic
ultracontractivity to nonsymmetric semigroups. In this paper, we study the
intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued
drifts and measure-valued potentials in bounded domains. Our process $Y$ is a
diffusion process whose generator can be formally written as
$L+\mu\cdot\nabla-\nu$ with Dirichlet boundary conditions, where $L$ is a
uniformly elliptic second-order differential operator and
$\mu=(\mu^1,...,\mu^d)$ is such that each component $\mu^i$, $i=1,...,d$, is a
signed measure belonging to the Kato class $\mathbf{K}_{d,1}$ and $\nu$ is a
(nonnegative) measure belonging to the Kato class $\mathbf{K}_{d,2}$. We show
that scale-invariant parabolic and elliptic Harnack inequalities are valid for
$Y$. In this paper, we prove the parabolic boundary Harnack principle and the
intrinsic ultracontractivity for the killed diffusion $Y^D$ with measure-valued
drift and potential when $D$ is one of the following types of bounded domains:
twisted H\"{o}lder domains of order $\alpha\in(1/3,1]$, uniformly H\"{o}lder
domains of order $\alpha\in(0,2)$ and domains which can be locally represented
as the region above the graph of a function. This extends the results in [J.
Funct. Anal. 100 (1991) 181--206] and [Probab. Theory Related Fields 91 (1992)
405--443]. As a consequence of the intrinsic ultracontractivity, we get that
the supremum of the expected conditional lifetimes of $Y^D$ is finite.

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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg