The Calderón projector for an elliptic operator in divergence form.
type: Item
instance of: scholarly article
title: The Calderón projector for an elliptic operator in divergence form.
zbMATH Open document ID: 1137.35350
DOI: 10.1007/BF02513079
author: Marcela Sanmartino
published in: The Journal of Fourier Analysis and Applications
publication date: 2002-06-19T00:00:00Z
full work available at URL: https://eudml.org/doc/59701
review text: The Calderón projector was first introduced by Calderón in [Lecture Notes on pseudodifferential operators and boundary value problems, I. A. M. CONICET, Bs. As.], for elliptic operators with \(C^{\infty}\) coefficients in a \(C^{\infty}\) domain. For the Laplace operator, the results of \textit{E. B. Fabes}, \textit{M. Jodeit jun.} and \textit{N. M. Rivière}, Acta Math. 141, 165--186 (1978; Zbl 0402.31009)] show that, on \(C^1\) domains, the Calderón projector is bounded on \(L^p(\partial\Omega)\times L^p(\partial\Omega)\) for all \(1<p<+\infty\). In the present paper, similar results are obtained for second order elliptic operators in divergence form \(L=-\text{div }A\nabla\) on \(C^1\) domains when the entries of \(A\) are Lipschitz functions. The construction is done by means of the layer potentials.
reviewed by: Emmanuel Russ
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35C15
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 1757477
zbMATH Keywords: elliptic boundary value problems
zbMATH Keywords: layer potentials
zbMATH Keywords: Lipschitz coefficients
zbMATH Keywords: Lipschitz domains
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1757477