He trace of BV-functions on an irregular subset

Yury D. Burago, N. N. Kosovskiǐ

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Certain basic results on the boundary trace discussed in Maźya's monograph on Sobolev spaces are generalized to a wider class of regions. The paper is an extended and supplemented version of a preliminary publication, where some results were presented without proofs or in a weaker form. In Maźya's monograph, the boundary trace was defined for regions Ω with finite perimeter, and the main results were obtained under the assumption that normals in the sense of Federer exist almost everywhere on the boundary. Instead, now it is assumed that the region boundary is a countably (n - 1)-rectifiable set, which is a more general condition.

Original languageEnglish (US)
Pages (from-to)251-266
Number of pages16
JournalSt. Petersburg Mathematical Journal
Volume22
Issue number2
DOIs
StatePublished - Dec 1 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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