New classes of non-smooth bounded domains D , for which the embedding operator from H 1 (D) into L 2 (D) is compact, are introduced. These classes include, in particular, the domains whose boundary locally are graphs of C-functions, but also contain much larger classes of domains. Examples of non-smooth domains for which the above embedding is compact are given. Applications to scattering by rough obstacles are mentioned.
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ol'dshtein et al. (2001) studied this question.