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

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 Lam\'e operator $-\Delta^\ast$. This improves upon the previous result in \cite{BFRVV} which relies on a stronger condition to guarantee the self-adjointness of $-\Delta^\ast$. Furthermore, by establishing local energy estimates for the elastic wave equation we also prove that the solution has local regularity.