Capacitary estimates of solutions of semilinear parabolic equations
type: Item
instance of: scholarly article
title: Capacitary estimates of solutions of semilinear parabolic equations
zbMATH Open document ID: 1282.35105
author: Laurent Véron
author: Moshe Marcus
published in: Calculus of Variations and Partial Differential Equations
publication date: 2013-09-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/0709.4106
review text: This paper is concerned with estimates for solutions of the semilinear parabolic equation \(u_t-\Delta u+u^q=0\) in \(\mathbb R^N\times (0,\infty)\), \(q>1\). The authors obtain that any positive solution for this equation with initial trace \((F,0)\), where \(F\subset\mathbb R^N\) is a closed set, can be represented up to two universal multiplicative constants by a series involving the \(C_{2/q,q'}\)-Bessel capacity. As a consequence, the uniqueness of such a solution is deduced. Next, the authors characterize the blow-up set of \(u(x,t)\) as \(t\to 0\) using the density of the set \(F\) expressed in terms of the \(C_{2/q,q'}\)-Bessel capacity.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 31C15
Mathematics Subject Classification ID: 31B10
Mathematics Subject Classification ID: 31C40
Mathematics Subject Classification ID: 35K58
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 6210451
zbMATH Keywords: Bessel capacitary
zbMATH Keywords: blow-up set
MaRDI profile type: Publication
OpenAlex ID: W2027343765
arXiv ID: 0709.4106
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DOI: 10.1007/S00526-012-0545-9
description: scientific article; zbMATH DE number 6210451