论文标题
具有单数电位的弹性波方程的Strichartz估计和局部规律性
Strichartz estimates and local regularity for the elastic wave equation with singular potentials
论文作者
论文摘要
我们获得了弹性波方程的加权$ l^2 $估计值，这些弹性波方程受到奇异电位的扰动，包括反方势。然后，我们根据lamé操作员$-Δ^ast $的唯一椭圆状条件下推断出Strichartz的估计。这在\ cite {bfrvv}的先前结果上得到了改善，\ cite {bfrvv}依赖于更强的条件来保证$-Δ^\ ast $的自相关性。此外，通过建立弹性波方程的局部能量估计，我们还证明该解决方案具有局部规律性。
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 Lamé operator $-Δ^\ast$. This improves upon the previous result in \cite{BFRVV} which relies on a stronger condition to guarantee the self-adjointness of $-Δ^\ast$. Furthermore, by establishing local energy estimates for the elastic wave equation we also prove that the solution has local regularity.
