Stability of the unique continuation for the wave operator via Tataru inequality : the local case

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Bosi , R , Kurylev , Y & Lassas , M 2018 , ' Stability of the unique continuation for the wave operator via Tataru inequality : the local case ' , Journal d'Analyse Mathematique , vol. 134 , no. 1 , pp. 157-199 . https://doi.org/10.1007/s11854-018-0006-2

Title: Stability of the unique continuation for the wave operator via Tataru inequality : the local case
Author: Bosi, Roberta; Kurylev, Yaroslav; Lassas, Matti
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2018-02
Language: eng
Number of pages: 43
Belongs to series: Journal d'Analyse Mathematique
ISSN: 0021-7670
URI: http://hdl.handle.net/10138/311064
Abstract: In 1995, Tataru proved a Carleman-type estimate for linear operators with partially analytic coefficients that is generally used to prove the unique continuation of those operators. In this paper, we use this inequality to study the stability of the unique continuation in the case of the wave equation with coefficients independent of time. We prove a logarithmic estimate in a ball whose radius has an explicit dependence on the C (1)-norm of the coefficients and on the other geometric properties of the operator.
Subject: INVERSE PROBLEM
COEFFICIENTS
EQUATIONS
111 Mathematics
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