Compactness of the embedding operators for rough domains

Vladimir Gol'dshtein, Alexander G. Ramin

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


New classes of non-smooth bounded domains D, for which the embedding operator from II1(D) into L2(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 arc mentioned.

Original languageEnglish
Pages (from-to)127-141
Number of pages15
JournalMathematical Inequalities and Applications
Issue number1
StatePublished - 1 Jan 2001


  • Embedding theorems
  • Quasiconformal mappings
  • Rough domains
  • Sobolev spaces

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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