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Traces of functions of generalized Sobolev classes

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Abstract

Considering the Sobolev type function classes on a metric space equipped with a Borel measure we address the question of compactness of embeddings of the space of traces into Lebesgue spaces on the sets of less “dimension.” Also, we obtain compactness conditions for embeddings of the traces of the classical Sobolev spaces W 1 p on the “zero” cusp with a Hölder singularity at the vertex.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. S. Romanov

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  1. A. S. Romanov
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__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 4, pp. 848–866, July–August, 2007.

Original Russian Text Copyright © 2007 Romanov A. S.

The author was supported by the Russian Foundation for Basic Research (Grant 05-01-00482a), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-8526.2006.1), and the Integration Grant of the Siberian Division of the Russian Academy of Sciences, 2006.

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Romanov, A.S. Traces of functions of generalized Sobolev classes. Sib Math J 48, 678–693 (2007). https://doi.org/10.1007/s11202-007-0070-9

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  • DOI: https://doi.org/10.1007/s11202-007-0070-9

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