Artículos de revistas
Time-weighted Estimates In Lorentz Spaces And Self-similarity For Wave Equations With Singular Potentials
Registro en:
Analysis And Pde. Mathematical Sciences Publishers, v. 10, n. 2, p. 423 - 438, 2017.
2157-5045
10.2140/apde.2017.10.423
2-s2.0-85014707663
Autor
De Almeida M.F.
Ferreira L.C.F.
Institución
Resumen
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. 10 2 423 438