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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 6, Pages 1298–1315
(Mi smj2162)
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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
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
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
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https://www.mathnet.ru/eng/smj2162 https://www.mathnet.ru/eng/smj/v51/i6/p1298
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Abstract page: | 311 | Full-text PDF : | 121 | References: | 100 |
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