Israel Journal of Mathematics

, Volume 123, Issue 1, pp 61–92 | Cite as

Sobolev inequalities of exponential type



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 log an 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.


SOBOLEV Inequality Orlicz Space Exponential Type Orlicz Function Irregular Domain 
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Copyright information

© The Hebrew University Magnes Press 2001

Authors and Affiliations

  1. 1.Centre for Mathematical Analysis and Its ApplicationsUniversity of SussexBrightonU.K.
  2. 2.Department of MathematicsUniversity of HelsinkiFinland

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