论文标题
持有人电势的半经典解析估计
Semiclassical resolvent estimates for Holder potentials
论文作者
论文摘要
我们首先证明了r d，d $ \ ge $ 3中的schr {Ö} dinger操作员的半经典分解估计值，相对于径向变量，具有实值的电位。然后，我们将这些分解估计值扩展到R d，d $ \ ge $ 2的外部域，以及相对于空间变量而言是H {Ö} lder的实价电势。作为一种应用，我们通过折射索引获得了溶液对波方程的局部能量的衰减速率，该指数可能是h {Ö} lder，lipschitz或仅是l $ \ infty $。
We first prove semiclassical resolvent estimates for the Schr{ö}dinger operator in R d , d $\ge$ 3, with real-valued potentials which are H{ö}lder with respect to the radial variable. Then we extend these resolvent estimates to exterior domains in R d , d $\ge$ 2, and real-valued potentials which are H{ö}lder with respect to the space variable. As an application, we obtain the rate of the decay of the local energy of the solutions to the wave equation with a refraction index which may be H{ö}lder, Lipschitz or just L $\infty$ .
