Sobolev inequalities of exponential type
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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.
KeywordsSOBOLEV Inequality Orlicz Space Exponential Type Orlicz Function Irregular Domain
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