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

Eva Sincich; Sergio Vessella

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arXiv · 1603.08778

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

Eva Sincich·Sergio Vessella

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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 $u_{\mid S}$ on $S$ is flat on a segment $\{0\}\times J$ with $0\in S$ then $u_{\mid S}$ vanishes in a neighborhood of $\{0\}\times J$.

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Eva Sincich, Sergio Vessella. 2016-03-29. Wave equation with Robin condition, quantitative estimates of strong unique continuation at the boundary. https://arxiv.org/abs/1603.08778

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