Some dispersive estimates for Schrödinger equations with repulsive potentials |
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Authors: | Juan A. Barceló ,Luis Vega |
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Affiliation: | a ETSI de Caminos, Universidad Politécnica de Madrid, 28040 Madrid, Spain b Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain c Departamento de Matemáticas, Universidad del Pais Vasco, Apartado 644, 48080 Bilbao, Spain |
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Abstract: | We prove the local smoothing effect for Schrödinger equations with repulsive potentials for n?3. The estimates are global in time and are proved using a variation of Morawetz multipliers. As a consequence we give sharp constants to measure the attractive part of the potential and its rate of decay, which turns out to be different whether dimension 3 or higher are considered. Also a notion of zero resonance arises in a natural way. Our smoothing estimate allows us to use Sobolev inequalities and treat nonradial perturbations. |
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Keywords: | Schrö dinger equations Dispersive estimates Energy methods |
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