Essential norms and localization moduli of Sobolev embeddings for general domains |
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Authors: | Lang J; Maz'ya V |
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Institution: | Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus, OH 43210 USA |
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Abstract: | We introduce new measures of non-compactness for the embeddingoperator Ep,q():Lp1() Lq() and describe their relations withthe essential norm of Ep, q(), local isoperimetricand isocapacitary constants. An explicit formula for the essentialnorm of Ep, q() is obtained for domains with a power cusp onthe boundary and bounded C1 domains. The Neumann problem fora particular Schrödinger operator is discussed on domainswith a power cusp. |
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