Dispersive type estimates for Fourier integrals and applications to hyperbolic systems

Details Dispersive type estimates for Fourier integrals and applications to hyperbolic systems Dispersive type estimates for Fourier integrals and applications to hyperbolic systems

2010-06-29

arxiv.org/abs/1006.5600v1

Disc. Cont. Dyn. Systems, Suppl. (2011), 1263--1270

Mathematics

Analysis of PDEs

8 pages

Scientific paper

In this note we provide dispersive estimates for Fourier integrals with parameter-dependent phase functions in terms of geometric quantities of associated families of Fresnel surfaces. The results are based on a multi-dimensional van der Corput lemma due to the first author. Applications to dispersive estimates for hyperbolic systems and scalar higher order hyperbolic equations are also discussed.

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