A Vector Field Method on the Distorted Fourier Side and Decay for Wave Equations With Potentials - Brossura

Donninger, Roland; Krieger, Joachim

Brossura

ISBN 10: 1470418738 ISBN 13: 9781470418731

Casa editrice: Amer Mathematical Society, 2016

Riassunto

The authors study the Cauchy problem for the one-dimensional wave equation ∂ 2 t u (t , x) - ∂ 2 x u (t , x) V (x)u (t , x) = 0. The potential V is assumed to be smooth with asymptotic behavior V (x) ∼ - 1 4 |x|-2 as |x| →∞. They derive dispersive estimates, energy estimates, and estimates involving the scaling vector field t ∂t x∂x , where the latter are obtained by employing a vector field method on the “distorted” Fourier side. In addition, they prove local energy decay estimates. Their results have immediate applications in the context of geometric evolution problems. The theory developed in this paper is funda­mental for the proof of the co-dimension 1 stability of the catenoid under the vanishing mean curvature flow in Minkowski space; see Donninger, Krieger, Szeftel, and Wong, “Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space”, preprint arXiv:1310.5606 (2013).

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 1470418738
• ISBN 13: 9781470418731
• Rilegatura: Copertina flessibile
• Numero di pagine: 80
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile