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Strichartz estimates for the wave and Schrödinger equations with potentials of critical decay. (English) Zbl 1084.35014
Summary: We prove weighted \(L^2\) estimates for the solutions of linear Schrödinger and wave equations with potentials that decay like \(|x|^{-2}\) for large \(x\), by deducing them from estimates on the resolvent of the associated elliptic operator. We then deduce Strichartz estimates for these equations.

MSC:
35B45 A priori estimates in context of PDEs
35L15 Initial value problems for second-order hyperbolic equations
35Q40 PDEs in connection with quantum mechanics
35L05 Wave equation
35G10 Initial value problems for linear higher-order PDEs
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