Strichartz estimates for the Schrödinger equation with a measure-valued potential

Erdoğan, M.; Goldberg, Michael; Green, William

doi:10.1090/bproc/79

Strichartz estimates for the Schrödinger equation with a measure-valued potential
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by M. Burak Erdoğan, Michael Goldberg and William R. Green HTML | PDF

Proc. Amer. Math. Soc. Ser. B 8 (2021), 336-348

Abstract:

We prove Strichartz estimates for the Schrödinger 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 Schrödinger evolution.

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