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Other literature type . 1994
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Local regularity of solutions to wave equations with time-dependent potentials

Local regularity of solutions to wave equations with time-dependent potentials
descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Dec 1994Publisher:Duke University PressJournal:Duke Mathematical Journal, volume 76 (issn: 0012-7094, Copyright policy )
Authors: Ruiz, Alberto; Vega, Luis;

doi: 10.1215/s0012-7094-94-07636-9

Local regularity of solutions to wave equations with time-dependent potentials

Abstract

The authors continue the investigation they started in the proceeding paper [\textit{A. Ruiz} and \textit{L. Vega}, Int. Math. Res. Not. 1993, No. 1, 13-27 (1993; Zbl 0812.35016)]. Here, they give the weighted estimates of the solutions to the initial value problems for the time-dependent Schrödinger equation and for the wave equation in the Lorentz spaces. Using the above results they prove the local existence, uniqueness and regularity of the above problems perturbed by time-dependent potentials with singularities.

Keywords

time-dependent potentials with singularities, 35L15, 35B65, Smoothness and regularity of solutions to PDEs, 35J10, Perturbation theories for operators and differential equations in quantum theory, Schrödinger equation, wave equation, Helmholtz equation, Local existence and uniqueness theorems (PDE)

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
31
Top 10%
Top 10%
Average
Green