Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirichlet forms and semilinear elliptic equations with measure data   We propose a probabilistic definition of solutions of semilinear elliptic
equations with (possibly nonlocal) operators associated with regular Dirichlet
forms and with measure data. Using the theory of backward stochastic
differential equations we prove the existence and uniqueness of solutions in
the case where the right-hand side of the equation is monotone and satisfies
mild integrability assumption, and the measure is smooth. We also study
regularity of solutions under the assumption that the measure is smooth and has
finite total variation. Some applications of our general results are given.

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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
1
The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn