The Laplacian with Wentzell-Robin boundary conditions on spaces of continuous functions
type: Item
instance of: scholarly article
title: The Laplacian with Wentzell-Robin boundary conditions on spaces of continuous functions
zbMATH Open document ID: 1073.47045
author: Wolfgang Arendt
author: Silvia Romanelli
author: Giorgio Metafune
author: Diego Pallara
published in: Semigroup Forum
publication date: 2004-03-07T00:00:00Z
review text: The authors study the Laplacian \(\Delta\) on a smooth bounded domain \(\Omega\subset {\mathbb R}^n\) with Wentzell-Robin boundary condition \(\beta u +\frac{\partial u}{\partial \nu} +\Delta u=0\) on the boundary \(\Gamma\). The aim is to show that the operator generates a positive differentiable contraction semigroup on \(C(\bar\Omega)\). For this, the authors use the method of quadratic forms to construct a semigroup on \(L^2(\Omega)\oplus L^2(\Gamma)\) and show that it is a Markov semigroup, thus extendable to \(L^p(\Omega)\oplus L^p(\Gamma),\;1\leq p<\infty\). By means of Schauder estimates it is then proved that the semigroup is a Feller semigroup on \(C(\bar\Omega)\). Some monotonicity properties and the asymptotic behaviour are established.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 2051543
zbMATH Keywords: Laplacian
zbMATH Keywords: Wentzell-Robin boundary condition
zbMATH Keywords: method of quadratic forms
zbMATH Keywords: Schauder estimates
zbMATH Keywords: monotonicity
zbMATH Keywords: asymptotic behaviour
reviewed by: V. A. Liskevich
MaRDI profile type: Publication
full work available at URL: s00233-002-0010-8
OpenAlex ID: W2033205460
DOI: 10.1007/S00233-002-0010-8
description: scientific article; zbMATH DE number 2051543