Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conservativeness criteria for generalized Dirichlet forms   We develop sufficient analytic conditions for conservativeness of
non-sectorial perturbations of symmetric Dirichlet forms which can be
represented through a carr\'e du champ on a locally compact separable metric
space. These form an important subclass of generalized Dirichlet forms which
were introduced in \cite{St1}. In case there exists an associated strong Feller
process, the analytic conditions imply conservativeness, i.e. non-explosion of
the associated process in the classical probabilistic sense. As an application
of our general results on locally compact separable metric state spaces, we
consider a generalized Dirichlet form given on a closed or open subset of
$\mathbb{R}^d$ which is given as a divergence free first order perturbation of
a symmetric energy form. Then using volume growth conditions of the carr\'e du
champ and the non-sectorial first order part, we derive an explicit criterion
for conservativeness. We present several concrete examples which relate our
results to previous ones obtained by different authors. In particular, we show
that conservativeness can hold for a cubic variance if the drift is strong
enough to compensate it. This work continues our previous work on transience
and recurrence of generalized Dirichlet forms.

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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph