A Vector Field Method on the Distorted Fourier Side and Decay for Wave Equations With Potentials (Memoirs of the American Mathematical Society, Band 1142) - Softcover

Donninger, Roland; Krieger, Joachim

 
9781470418731: A Vector Field Method on the Distorted Fourier Side and Decay for Wave Equations With Potentials (Memoirs of the American Mathematical Society, Band 1142)
Softcover
ISBN 10: 1470418738 ISBN 13: 9781470418731
Verlag: American Mathematical Society, 2016

Inhaltsangabe

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).

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Über die Autorin bzw. den Autor

Roland Donninger, and Joachim Krieger, Ecole Polytechnique Federale de Lausanne, Switzerland.

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Verlag
American Mathematical Society
Erscheinungsdatum
2016
Sprache
Englisch
ISBN 10 
1470418738
ISBN 13 
9781470418731
Einband
Taschenbuch
Anzahl der Seiten
80
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Verantwortliche Person
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