STRICHARTZ ESTIMATES AND LOCAL REGULARITY FOR THE ELASTIC WAVE EQUATION WITH SINGULAR POTENTIALS

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 Lame operator -Delta*. This improves upon the previous result in [1] which relies on a stronger condition to guarantee the self-adjointness of -Delta*. Furthermore, by establishing local energy estimates for the elastic wave equation we also prove that the solution has local regularity.

Automated summary

In this work, we obtain weighted L-2 estimates for the elastic wave equation perturbed by singular potentials, including the inverse-square potential. Additionally, we deduce Strichartz estimates under the sole ellipticity condition for the Lame operator -Delta*, improving upon previous results which required a stronger condition for ensuring self-adjointness of -Delta*. Furthermore, by establishing local energy estimates for the elastic wave equation, we also demonstrate that the solution possesses local regularity.