Some inequalities related to isoperimetric inequalities with partial free boundary

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dc.creatorZhu, Meijun
dc.date2001-01-09
dc.date2001-02-16
dc.date.accessioned2026-07-07T04:39:35Z
dc.date.available2026-07-07T04:39:35Z
dc.descriptionThe main purpose of this paper is to prove a sharp Sobolev inequality in an exterior of a convex bounded domain. There are two ingredients in the proof: One is the observation of some new isoperimetric inequalities with partial free boundary, and the other is an integral inequality (due to Duff [9]) for any nonnegative function under Schwarz equimeasurable rearrangement. These ingredients also allow us to establish some Moser-Trudinger type inequalities, and obtain some estimates on the principal frequency of a membrane with partial free boundary, which extend early results of Nehari [15] and Bandle [5] for two dimensional domains to the one for any dimensional domains (dimension $\ge 2$)
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/math/0101078
dc.identifierhttp://arxiv.org/abs/math/0101078
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60726
dc.subjectAnalysis of PDEs
dc.subjectClassical Analysis and ODEs
dc.subjectDifferential Geometry
dc.titleSome inequalities related to isoperimetric inequalities with partial free boundary
dc.typetext

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