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arXiv · 2007.03256

Strichartz estimates and local regularity for the elastic wave equation with singular potentials

Seongyeon Kim·Yehyun Kwon·Ihyeok Seo
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Abstract

We obtain weighted $L^2$ estimates for the elastic wave equation perturbed by singular potentials including the inverse-square potential. We then deduce the Strichartz estimates under the sole ellipticity condition for the Lamé operator $-Δ^\ast$. This improves upon the previous result in \cite{BFRVV} which relies on a stronger condition to guarantee the self-adjointness of $-Δ^\ast$. Furthermore, by establishing local energy estimates for the elastic wave equation we also prove that the solution has local regularity.

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Seongyeon Kim, Yehyun Kwon, Ihyeok Seo. 2020-08-24. Strichartz estimates and local regularity for the elastic wave equation with singular potentials. https://arxiv.org/abs/2007.03256

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