Some remarks on the characterization of the space of tangential traces of \(H(\text{rot}; \Omega)\) and the construction of an extension operator
type: Item
instance of: scholarly article
title: Some remarks on the characterization of the space of tangential traces of \(H(\text{rot}; \Omega)\) and the construction of an extension operator
zbMATH Open document ID: 0856.46019
DOI: 10.1007/BF02567511
author: Alberto Valli
author: Ana M. Alonso Rodriguez
published in: Manuscripta Mathematica
publication date: 1997-01-27T00:00:00Z
full work available at URL: https://eudml.org/doc/156156
review text: Let \(\Omega\) be a connected, bounded, open subset of \(R^3\), and \(H(\text{rot}; \Omega)\) be a space of the vector functions \(\phi\in (L^2(\Omega))^3\) such that \(\text{rot } \phi\in (L^2(\Omega))^3\). The tangential trace on \(\partial\Omega\) of \(u\in H(\text{rot}; \Omega)\) is \(n\times u_{|\partial\Omega}\) for the unit outward normal vector of \(\partial\Omega\). The authors deal with the space of tangential traces of functions belonging to \(H(\text{rot}; \Omega)\) and construct a linear and continuous extension operator from this trace to \(H(\text{rot}; \Omega)\). They consider also tangential traces on a proper subset of \(\partial\Omega\) and construct corresponding extension operators. Two other results are a solvability theorem for the so-called Dirichlet harmonic vector fields and an existence theorem for a mixed Dirichlet-Neumann boundary value problem.
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 866129
zbMATH Keywords: tangential trace
zbMATH Keywords: Dirichlet harmonic vector fields
zbMATH Keywords: mixed Dirichlet-Neumann boundary value problem
reviewed by: Valery Borisovich Marenich
MaRDI profile type: Publication
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OpenAlex ID: W2029243375
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description: scientific article; zbMATH DE number 866129