Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev
  Diffusion Coefficients   In this paper we prove the stochastic homeomorphism flow property and the
strong Feller property for stochastic differential equations with sigular time
dependent drifts and Sobolev diffusion coefficients. Moreover, the local well
posedness under local assumptions are also obtained. In particular, we extend
Krylov and R\"ockner's results in \cite{Kr-Ro} to the case of non-constant
diffusion coefficients.

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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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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: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: physics