Essential norms and localization moduli of Sobolev embeddings for general domains

• Autores: J. Lang, Vladimir G. Maz'ya
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 78, Nº 2, 2008, págs. 373-391
• Idioma: inglés
• DOI: 10.1112/jlms/jdn035
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• Resumen

  • We introduce new measures of non-compactness for the embedding operator Ep,q():Lp1() Lq() and describe their relations with the essential norm of Ep, q(), �local� isoperimetric and isocapacitary constants. An explicit formula for the essential norm of Ep, q() is obtained for domains with a power cusp on the boundary and bounded C1 domains. The Neumann problem for a particular Schrödinger operator is discussed on domains with a power cusp