Conductor Sobolev-type estimates and isocapacitary inequalities
Cerdà Martín, Joan Lluís (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
Martín i Pedret, Joaquim (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Silvestre, Pilar (Aalto University. Department of Mathematics and Systems Analysis)

Date:	2012
Abstract:	In this paper we present an integral inequality connecting a function space (quasi-)norm of the gradient of a function to an integral of the corresponding capacity of the conductor between two level surfaces of the function, which extends the estimates obtained by V. Maz'ya and S. Costea, and sharp capacitary inequalities due to V. Maz'ya in the case of the Sobolev norm. The inequality, obtained under appropriate convexity conditions on the function space, gives a characterization of Sobolev-type inequalities involving two measures, necessary and sufficient conditions for Sobolev isocapacitary-type inequalities, and self-improvements for integrability of Lipschitz functions.
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Language:	Anglès
Document:	Article ; Versió publicada
Subject:	Convexity ; Lower estimates ; Sobolev spaces ; Rearrangement invariant spaces ; Sobolev-type inequalities
Published in:	Indiana University mathematics journal, Vol. 61, No. 5 (2012) , p. 1925-1947, ISSN 0022-2518

DOI: 10.1512/iumj.2012.61.4709

23 p, 217.4 KB

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