We prove a sharp resolvent estimate in scale invariant norms of Amgon–Hörmander type for a magnetic Schrödinger operator on Rn, n ≥ 3 L = −(∂ + iA)2 + V with large potentials A, V of almost critical decay and regularity. The estimate is applied to prove sharp smoothing and Strichartz estimates for the Schrödinger, wave and Klein–Gordon flows associated to L.
On large potential perturbations of the Schrödinger, Wave and Klein–Gordon equations / D'Ancona, P.. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 19:1(2020), pp. 609-640. [10.3934/cpaa.2020029]
On large potential perturbations of the Schrödinger, Wave and Klein–Gordon equations
D'Ancona P.
Membro del Collaboration Group
2020
Abstract
We prove a sharp resolvent estimate in scale invariant norms of Amgon–Hörmander type for a magnetic Schrödinger operator on Rn, n ≥ 3 L = −(∂ + iA)2 + V with large potentials A, V of almost critical decay and regularity. The estimate is applied to prove sharp smoothing and Strichartz estimates for the Schrödinger, wave and Klein–Gordon flows associated to L.File allegati a questo prodotto
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