Resumen de Essential norms and localization moduli of Sobolev embeddings for general domains

J. Lang, Vladimir G. Maz'ya

• 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