\(BV\) functions and parabolic initial boundary value problems on domains
type: Item
instance of: scholarly article
title: \(BV\) functions and parabolic initial boundary value problems on domains
zbMATH Open document ID: 1177.35105
author: Luciana Angiuli
author: Fabio Paronetto
author: Michele jun. Miranda
author: Diego Pallara
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2009-10-02T00:00:00Z
review text: The authors consider semigroup \((T(t))_{t\geq 0}\) generated by a uniformly elliptic second order operator \(A\) in \(L^1(\Omega)\) under homogeneous co-normal boundary conditions on \(\partial\Omega.\) It is shown that the limit as \(t\to 0\) of the \(L^1\)-norm of \(D_x T(t)u_0\) tends to the total variation of the initial datum \(u_0,\) and in particular is finite if and only if \(u_0\) belongs to \(BV(\Omega)\) or weighted \(BV\) spaces.
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 49Q15
zbMATH DE Number: 5610627
zbMATH Keywords: linear parabolic equations
zbMATH Keywords: BV functions
zbMATH Keywords: semigroup theory
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: s10231-008-0076-3
OpenAlex ID: W2032771947
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DOI: 10.1007/S10231-008-0076-3
description: scientific article; zbMATH DE number 5610627