Carleman estimates and unique continuation for solutions to boundary value problems
type: Item
instance of: scholarly article
title: Carleman estimates and unique continuation for solutions to boundary value problems
zbMATH Open document ID: 0896.35023
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1998-10-11T00:00:00Z
review text: Let \(K\) be a domain in \(\mathbb{R}^n\) and \(S\) a smooth surface that intersects \(\partial K\) and divides \(K\) into two parts. The paper is devoted to establishing Carleman-type inequalities for solutions \(u\) of very general boundary value problems. These inequalities imply that (i) \(u\) can be uniquely continued across \(S\) and (ii) the regularity properties of \(u\) ``extend across \(S\)''. The hypotheses involved are, apart from a relaxed pseudoconvexity condition on \(S\), what the author calls a strong or an \(r\)-strong Lopatinskiĭ condition for the boundary operator with respect to a point of \(S\cap\partial K\). The paper is necessarily quite technical, but the assumptions are illustrated for the wave, Schrödinger, and plate equations.
Mathematics Subject Classification ID: 35B60
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35G15
zbMATH DE Number: 917931
zbMATH Keywords: relaxed pseudoconvexity condition
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: wave equation
zbMATH Keywords: plate equations
author: Daniel Tataru
reviewed by: Hubert Kalf
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 917931