The main result of the present paper consists in a quantitative estimate of unique continuation at the boundary for solutions to the wave equation. Such estimate is the sharp quantitative counterpart of the following strong unique continuation property: let u be a solution to the wave equation that satisfies an homogeneous Robin condition on a portion S of the boundary and the restriction of u|S on S is flat on a segment {0} × J with 0 \in S then u|S vanishes in a neighborhood of {0} × J.

Wave equation with Robin condition, quantitative estimates of strong unique continuation at the boundary / Sincich, Eva; Vessella, Sergio. - In: RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE. - ISSN 0049-4704. - STAMPA. - 48:(2016), pp. 221-243. [10.13137/2464-8728/13158]

Wave equation with Robin condition, quantitative estimates of strong unique continuation at the boundary

VESSELLA, SERGIO
2016

Abstract

The main result of the present paper consists in a quantitative estimate of unique continuation at the boundary for solutions to the wave equation. Such estimate is the sharp quantitative counterpart of the following strong unique continuation property: let u be a solution to the wave equation that satisfies an homogeneous Robin condition on a portion S of the boundary and the restriction of u|S on S is flat on a segment {0} × J with 0 \in S then u|S vanishes in a neighborhood of {0} × J.
2016
48
221
243
Sincich, Eva; Vessella, Sergio
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1036851
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