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Type: Artigo
Title: Time-weighted Estimates In Lorentz Spaces And Self-similarity For Wave Equations With Singular Potentials
Author: De Almeida M.F.
Ferreira L.C.F.
Abstract: We show time-weighted estimates in Lorentz spaces for the linear wave equation with singular potential. As a consequence, assuming radial symmetry on initial data and potentials, we obtain well-posedness of global solutions in critical weak-Lp spaces for semilinear wave equations. In particular, we can consider the Hardy potential V(x) = c|x|-2 for small |c|. Self-similar solutions are obtained for potentials and initial data with the right homogeneity. Our approach relies on performing estimates in the predual of weak-Lp, i.e., the Lorentz space L(p',1). © 2017 Mathematical Sciences Publishers.
Subject: Lorentz Spaces
Radial Symmetry
Singular Potentials
Wave Equations
Editor: Mathematical Sciences Publishers
Rights: fechado
Identifier DOI: 10.2140/apde.2017.10.423
Date Issue: 2017
Appears in Collections:Unicamp - Artigos e Outros Documentos

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