Intrinsic ultracontractivity of non-symmetric diffusion semigroups in bounded domains
type: Item
instance of: scholarly article
title: Intrinsic ultracontractivity of non-symmetric diffusion semigroups in bounded domains
zbMATH Open document ID: 1167.60017
author: Panki Kim
author: Renming Song
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2009-03-11T00:00:00Z
review text: Let \(E\) be a locally compact separable metric space and let \(m\) be a positive finite measure on \(E\) with support equal to \(E\). The authors extend first the concept of intrinsic ultracontractivity to non-symmetric absolutely continuous semigroups acting on \(L^2(E,m)\). Moreover, some applications of this notion are given. Then, they prove essentially that, the Dirichlet semigroups of non-symmetric second order elliptic operators in bounded Lipschitz domains of \(\mathbb{R}^d\), are intrinsic ultracontractive. To do this, they use as a bridge, the (symmetric) semigroup defined by the symmetric part of the initial Dirichlet form. Then they use the logarithmic Sobolev inequalities.
reviewed by: Mohamed Hmissi
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 60J45
zbMATH DE Number: 5528029
zbMATH Keywords: semigroups
zbMATH Keywords: diffusions
zbMATH Keywords: ultracontractivity
zbMATH Keywords: intrinsic ultracontractivity
zbMATH Keywords: invariant functions
zbMATH Keywords: logaritheoremic Sobolev inequality
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1232376165
OpenAlex ID: W2034119464
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DOI: 10.2748/TMJ/1232376165
description: scientific article; zbMATH DE number 5528029