The trace of $BV$-functions on an irregular subset
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Yu. D. Burago and N. N. KosovskiÄ
Translated by: the authors - St. Petersburg Math. J. 22 (2011), 251-266
- DOI: https://doi.org/10.1090/S1061-0022-2010-01139-7
- Published electronically: February 8, 2011
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Abstract:
Certain basic results on the boundary trace discussed in Mazâ˛yaâs 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 Mazâ˛yaâs monograph, the boundary trace was defined for regions $\Omega$ 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.References
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Bibliographic Information
- Yu. D. Burago
- Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, 27 Fontanka, St. Petersburg 191023, Russia
- Email: yuburago@pdmi.ras.ru
- N. N. KosovskiÄ
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, 28 Universitetskii Prospekt, Peterhoff, St. Petersburg 198504, Russia
- Email: kosovnn@pdmi.ras.ru
- Received by editor(s): May 20, 2009
- Published electronically: February 8, 2011
- Additional Notes: Partially supported by RFBR (grant no. 08-01-00079a)
- © Copyright 2010 American Mathematical Society
- Journal: St. Petersburg Math. J. 22 (2011), 251-266
- MSC (2010): Primary 46E35; Secondary 28A75
- DOI: https://doi.org/10.1090/S1061-0022-2010-01139-7
- MathSciNet review: 2668125