Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mosco convergence of Sobolev spaces and Sobolev inequalities for
  nonsmooth domains   We find extremely general classes of nonsmooth open sets which guarantee
Mosco convergence for corresponding Sobolev spaces and the validity of Sobolev
inequalities with a uniform constant. An important feature of our results is
that the conditions we impose on the open sets for Mosco convergence and for
the Sobolev inequalities are of the same nature, therefore it is easy to check
when both are satisfied.
  Our analysis is motivated, in particular, by the study of the stability of
the direct acoustic scattering problem with respect to the scatterer, which we
also discuss.
  Concerning Mosco convergence in dimension 3 or higher, our result extends all
those previously known in the literature. Concerning Sobolev inequalities, our
approach seems to be new and considerably simplifies the conditions previously
required for the stability of acoustic direct scattering problems.

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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys