Local regularity of solutions to wave equations with time-dependent potentials
type: Item
instance of: scholarly article
title: Local regularity of solutions to wave equations with time-dependent potentials
zbMATH Open document ID: 0826.35014
DOI: 10.1215/S0012-7094-94-07636-9
author: Alberto Ruiz
author: L. Vega
published in: Duke Mathematical Journal
publication date: 1995-06-11T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35A07
Mathematics Subject Classification ID: 81Q15
zbMATH DE Number: 755401
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: wave equation
zbMATH Keywords: time-dependent potentials with singularities
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 755401