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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 6, Pages 1298–1315 (Mi smj2162)  
This article is cited in 11 scientific papers (total in 11 papers)

Sufficiency of broken lines in the modulus method and removable sets

Yu. V. Dymchenko, V. A. Shlyk

Far Eastern National University, Vladivostok
Full-text PDF (403 kB) Citations (11)
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Abstract: We establish the sufficiency of the family of broken lines in calculating the modulus of a condenser. We extend the Ahlfors–Beurling definition of removable sets basing on rectangles to weighted Sobolev spaces with a Muckenhoupt weight. We obtain exact characteristics of removable sets in terms of girth by broken lines. We prove the invariance of weighted Sobolev spaces under quasi-isometric mappings.
Keywords: modulus of a family of curves, condenser capacity, Muckenhoupt weight, removable set, Sobolev space, quasi-isometry.
Received: 29.12.2009
Revised: 17.05.2010
English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 6, Pages 1028–1042
DOI: https://doi.org/10.1007/s11202-010-0101-9
Bibliographic databases:
Document Type: Article
UDC: 517.54+517.554
Language: Russian
Citation: Yu. V. Dymchenko, V. A. Shlyk, “Sufficiency of broken lines in the modulus method and removable sets”, Sibirsk. Mat. Zh., 51:6 (2010), 1298–1315; Siberian Math. J., 51:6 (2010), 1028–1042
Citation in format AMSBIB
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\paper Sufficiency of broken lines in the modulus method and removable sets
\jour Sibirsk. Mat. Zh.
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\vol 51
\issue 6
\pages 1298--1315
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\jour Siberian Math. J.
\yr 2010
\vol 51
\issue 6
\pages 1028--1042
\crossref{https://doi.org/10.1007/s11202-010-0101-9}
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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