Conductor inequalities and criteria for Sobolev-Lorentz two-weight inequalities

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dc.creatorCostea, Serban
dc.creatorMaz'ya, Vladimir
dc.date2008-04-18
dc.date.accessioned2026-07-07T09:33:29Z
dc.date.available2026-07-07T09:33:29Z
dc.descriptionIn this paper we present integral conductor inequalities connecting the Lorentz p,q-(quasi)norm of a gradient of a function to a one-dimensional integral of the p,q-capacitance of the conductor between two level surfaces of the same function. These inequalities generalize an inequality obtained by the second author in the case of the Sobolev norm. Such conductor inequalities lead to necessary and sufficient conditions for Sobolev-Lorentz type inequalities involving two arbitrary measures.
dc.descriptionv1: 15 pages
dc.identifierhttps://arxiv.org/abs/0804.3051
dc.identifierhttp://arxiv.org/abs/0804.3051
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159151
dc.subjectAnalysis of PDEs
dc.subject31C15, 46E35
dc.titleConductor inequalities and criteria for Sobolev-Lorentz two-weight inequalities
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