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arXiv · 1908.02903

Strichartz Estimates for the Schr\"odinger Equation with a Measure-Valued Potential

M. Burak Erdogan·Michael Goldberg·William R. Green
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Abstract

We prove Strichartz estimates for the Schr\"odinger equation in $\mathbb R^n$, $n\geq 3$, with a Hamiltonian $H = -\Delta + \mu$. The perturbation $\mu$ is a compactly supported measure in $\mathbb R^n$ with dimension $\alpha > n-(1+\frac{1}{n-1})$. The main intermediate step is a local decay estimate in $L^2(\mu)$ for both the free and perturbed Schr\"odinger evolution.

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M. Burak Erdogan, Michael Goldberg, William R. Green. 2019-08-08. Strichartz Estimates for the Schr\"odinger Equation with a Measure-Valued Potential. https://arxiv.org/abs/1908.02903

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