Log--Sobolev Inequalities and Regions with Exterior Exponential Cusps

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dc.creatorMason, C.
dc.date2001-07-12
dc.date.accessioned2026-07-07T04:42:34Z
dc.date.available2026-07-07T04:42:34Z
dc.descriptionWe begin by studying semigroup estimates that are more singular than those implied by a Sobolev embedding theorem but which are equivalent to certain logarithmic Sobolev inequalities. We then give a method for showing such log--Sobolev inequalities hold for Euclidean regions that satisfy a certain Hardy-type inequality. Our main application is to show that domains with exterior exponential cusps, and hence no Sobolev embedding theorem, satisfy such heat kernel bounds provided the cusp is not too sharp. Finally we consider a rotationally invariant domain with an exponentially sharp cusp and show that ultracontractivity does break down after a certain point.
dc.description20 pages. Submitted to J. Funct. Anal
dc.identifierhttps://arxiv.org/abs/math/0107088
dc.identifierhttp://arxiv.org/abs/math/0107088
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61838
dc.subjectSpectral Theory
dc.subject35P15, 35J25, 47A75, 47B25, 47D99
dc.titleLog--Sobolev Inequalities and Regions with Exterior Exponential Cusps
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