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|Title:||Time-weighted Estimates In Lorentz Spaces And Self-similarity For Wave Equations With Singular Potentials|
|Author:||De Almeida M.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.|
|Editor:||Mathematical Sciences Publishers|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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