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Sobolev inequalities of exponential type

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Abstract

We give sufficient conditions for domains to satisfy Sobolev inequalities of single exponential type. Earlier work in this area imposed more stringent conditions on the domains and is thus contained in our results. Moreover, the class of functions considered is based onL n logan L witha<1−1/n, n being the dimension of the underlying space. The limiting casea=1−1/n gives rise to an inequality of double exponential type which is shown to be valid in a large class of irregular domains. This inequality is new even in smooth domains.

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Authors and Affiliations

  1. Centre for Mathematical Analysis and Its Applications, University of Sussex, Falmer, BN1 9QH, Brighton, U.K.

    D. E. Edmunds

  2. Department of Mathematics, University of Helsinki, P.O. Box 4, FIN-00014, Finland

    R. Hurri-Syrjänen

Authors
  1. D. E. Edmunds
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  2. R. Hurri-Syrjänen
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Correspondence to D. E. Edmunds.

Additional information

The second author was partially supported by a grant from Magnus Ehrnrooth Foundation.

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Edmunds, D.E., Hurri-Syrjänen, R. Sobolev inequalities of exponential type. Isr. J. Math. 123, 61–92 (2001). https://doi.org/10.1007/BF02784120

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  • DOI: https://doi.org/10.1007/BF02784120

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