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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

The trace of $ BV$-functions on an irregular subset


Authors: Yu. D. Burago and N. N. Kosovskiĭ
Translated by: the authors
Original publication: Algebra i Analiz, tom 22 (2010), nomer 2.
Journal: St. Petersburg Math. J. 22 (2011), 251-266
MSC (2010): Primary 46E35; Secondary 28A75
Published electronically: February 8, 2011
MathSciNet review: 2668125
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Abstract: Certain basic results on the boundary trace discussed in Maz'ya'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 Maz'ya's 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.


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Additional 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. Kosovskiĭ
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, 28 Universitetskii Prospekt, Peterhoff, St. Petersburg 198504, Russia
Email: kosovnn@pdmi.ras.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2010-01139-7
PII: S 1061-0022(2010)01139-7
Keywords: Trace, rectifiability, perimeter, embedding theorems
Received by editor(s): May 20, 2009
Published electronically: February 8, 2011
Additional Notes: Partially supported by RFBR (grant no. 08-01-00079a)
Article copyright: © Copyright 2010 American Mathematical Society