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On the traces of Sobolev functions on the boundary of an anisotropic cusp

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Abstract

Given a “zero” cusp \(G_{\vec \lambda } \) with an anisotropic Hölder singularity at the vertex, we consider various embedding theorems for the Sobolev spaces \(W_p^1 (G_{\vec \lambda } )\) and the questions of embeddings of the traces of Sobolev functions into Lebesgue classes on the boundary of the cusp.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk, Russia

    A. S. Romanov

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  1. A. S. Romanov
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Correspondence to A. S. Romanov.

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Original Russian Text Copyright © 2011 Romanov A. S.

The author was supported by the Russian Foundation for Basic Research (Grant 10-01-00662-a).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 5, pp. 1150–1158, September–October, 2011.

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Romanov, A.S. On the traces of Sobolev functions on the boundary of an anisotropic cusp. Sib Math J 52, 914–920 (2011). https://doi.org/10.1134/S0037446611050168

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  • DOI: https://doi.org/10.1134/S0037446611050168

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