Hokkaido Mathematical Journal

D’Ancona Piero,

Smoothing and dispersive properties of evolution equations with potential perturbations.

Hokkaido Mathematical Journal, 37 (2008) pp.715-734

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Abstract

We survey a group of joint results with different authors concerning the decay properties of evolution equations with variable coefficients. The problems studied include the wave, Schrödinger and Dirac equation, perturbed with electromagnetic potentials, and the main focus of the paper is on global dispersive and Strichartz estimates when the coefficients are of low regularity and of critical decay.

MSC(Primary)35L05
MSC(Secondary)58J45
Uncontrolled Keywordshyperbolic equations, dispersive estimates, Strichartz estimates, dispersive equations, Schrödinger equation, Dirac equation, magnetic potential.