Strichartz and uniform Sobolev inequalities for the elastic wave equation
Analysis of PDEs
2022-08-31 v2 Classical Analysis and ODEs
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 Lam\'e 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.
Keywords
Cite
@article{arxiv.2102.04684,
title = {Strichartz and uniform Sobolev inequalities for the elastic wave equation},
author = {Seongyeon Kim and Yehyun Kwon and Sanghyuk Lee and Ihyeok Seo},
journal= {arXiv preprint arXiv:2102.04684},
year = {2022}
}
Comments
to appear in Proc. Amer. Math. Soc