STRICHARTZ ESTIMATES FOR THE SCHRÖDINGER EQUATION WITH A MEASURE-VALUED POTENTIAL

M. Burak Erdoğan; Michael Goldberg; William R. Green

doi:10.1090/bproc/79

STRICHARTZ ESTIMATES FOR THE SCHRÖDINGER EQUATION WITH A MEASURE-VALUED POTENTIAL

M. Burak Erdoğan, Michael Goldberg, William R. Green

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove Strichartz estimates for the Schrödinger equation in Rⁿ, n ě 3, with a Hamiltonian H “´Δ ` μ. The perturbation μ is a compactly supported measure in Rⁿ with dimension α ą n ´p1 `¹ q. The main n´1 intermediate step is a local decay estimate in L²pμq for both the free and perturbed Schrödinger evolution.

Original language	English (US)
Pages (from-to)	336-348
Number of pages	13
Journal	Proceedings of the American Mathematical Society, Series B
Volume	8
DOIs	https://doi.org/10.1090/bproc/79
State	Published - 2021

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1090/bproc/79

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abstract = "We prove Strichartz estimates for the Schr{\"o}dinger equation in Rn, n {\v e} 3, with a Hamiltonian H “´Δ ` μ. The perturbation μ is a compactly supported measure in Rn with dimension α {\c a} n ´p1 `1 q. The main n´1 intermediate step is a local decay estimate in L2pμq for both the free and perturbed Schr{\"o}dinger evolution.",

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N2 - We prove Strichartz estimates for the Schrödinger equation in Rn, n ě 3, with a Hamiltonian H “´Δ ` μ. The perturbation μ is a compactly supported measure in Rn with dimension α ą n ´p1 `1 q. The main n´1 intermediate step is a local decay estimate in L2pμq for both the free and perturbed Schrödinger evolution.

AB - We prove Strichartz estimates for the Schrödinger equation in Rn, n ě 3, with a Hamiltonian H “´Δ ` μ. The perturbation μ is a compactly supported measure in Rn with dimension α ą n ´p1 `1 q. The main n´1 intermediate step is a local decay estimate in L2pμq for both the free and perturbed Schrödinger evolution.

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STRICHARTZ ESTIMATES FOR THE SCHRÖDINGER EQUATION WITH A MEASURE-VALUED POTENTIAL

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