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

We obtain weighted L² 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 −∆^∗. This improves upon the previous result in [1] which relies on a stronger condition to guarantee the self-adjointness of −∆^∗. Furthermore, by establishing local energy estimates for the elastic wave equation we also prove that the solution has local regularity.