Strichartz and uniform Sobolev inequalities for the elastic wave equation

Kim, Seongyeon; Kwon, Yehyun; Lee, Sanghyuk; Seo, Ihyeok

doi:10.1090/proc/16101

Strichartz and uniform Sobolev inequalities for the elastic wave equation
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by Seongyeon Kim, Yehyun Kwon, Sanghyuk Lee and Ihyeok Seo

Proc. Amer. Math. Soc. 151 (2023), 239-253

DOI: https://doi.org/10.1090/proc/16101

Published electronically: September 23, 2022

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Abstract:

We prove dispersive estimate for the elastic wave equation by which we extend the known Strichartz estimates for the classical wave equation to those for the elastic wave equation. In particular, the endpoint Strichartz estimates are deduced. For the purpose we diagonalize the symbols of the Lamé operator and its semigroup, which also gives an alternative and simpler proofs of the previous results on perturbed elastic wave equations. Furthermore, we obtain uniform Sobolev inequalities for the elastic wave operator.

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