Isoperimetric Inequalities and Imbedding Theorems in Irregular Domains |
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Authors: | Hajlasz, Piotr Koskela, Pekka |
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Affiliation: | Instytut Matematyki, Uniwersytet Warszawski Banacha 2, 02-097 Warszawa, Poland. E-mail: hajlasz{at}mimuw.edu.pl Department of Mathematics, University of Michigan Ann Arbor, MI 48109, USA |
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Abstract: | The paper proves several weighted imbedding theorems for domainswith fractal boundaries. The weights considered are distancesto the boundary to certain powers, and the domains are so-calleds-John domains. The paper also proves, in the general setting,that the existence of an imbedding implies compactness of theimbedding for lower exponents. Moreover, following Maz'ya, thepaper reformulates the imbedding theorems in the language oflocal isoperimetric and capacity estimates. |
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