Capacitary estimates of positive solutions of semilinear elliptic equations with absorption
type: Item
instance of: scholarly article
title: Capacitary estimates of positive solutions of semilinear elliptic equations with absorption
zbMATH Open document ID: 1210.35112
DOI: 10.4171/JEMS/18
author: Laurent Véron
author: Moshe Marcus
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2005-02-28T00:00:00Z
review text: Summary: Let \(\Omega\) be a bounded domain of class \(C^2\) in \(\mathbb R^N\) and let \(K\) be a compact subset of \(\partial\Omega\). Assume that \(q\geq (N+1)/(N-1)\) and denote by \(U_K\) the maximal solution of \( -\Delta u+u^q=0\) in \(\Omega\) which vanishes on \(\partial\Omega\setminus K\). We obtain sharp upper and lower estimates for \(U_K\) in terms of the Bessel capacity \(C_{2/q,q'}\) and prove that \(U_K\) is \(\sigma\)-moderate. In addition we describe the precise asymptotic behavior of \(U_K\) at points \(\sigma\in K\), which depends on the `density' of \(K\) at \(\sigma\), measured in terms of the capacity \(C_{2/q,q'}\).
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35R05
zbMATH DE Number: 2139681
zbMATH Keywords: Bessel capacities, maximal solutions, rate of blow-up
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2139681