Strichartz estimates for the Schrödinger equation with a measure-valued potential
2021 ◽
Vol 8
(28)
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pp. 336-348
Keyword(s):
We prove Strichartz estimates for the Schrödinger equation in R n \mathbb {R}^n , n ≥ 3 n\geq 3 , with a Hamiltonian H = − Δ + μ H = -\Delta + \mu . The perturbation μ \mu is a compactly supported measure in R n \mathbb {R}^n with dimension α > n − ( 1 + 1 n − 1 ) \alpha > n-(1+\frac {1}{n-1}) . The main intermediate step is a local decay estimate in L 2 ( μ ) L^2(\mu ) for both the free and perturbed Schrödinger evolution.
2011 ◽
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(02)
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pp. 365-382
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pp. 246-303
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Vol 27
(7)
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pp. 1596-1601
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