The wave equation for the Bessel Laplacian
We study radial solutions of the Cauchy problem for the wave equation in the multidimensional unit ball Bd, d ≥ 1. In this case, the operator that appears is the Bessel Laplacian and the solution u (t, x) is given in terms of a Fourier-Bessel expansion. We prove that, for initial Lp data, the series...
| Authors: | , |
|---|---|
| Format: | article |
| Status: | Published version |
| Publication Date: | 2014 |
| Country: | España |
| Institution: | Universidad de La Rioja (UR) |
| Repository: | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| OAI Identifier: | oai:portal.dialnet.es:doc/5bbc69acb750603269e81f6e |
| Online Access: | https://investigacion.unirioja.es/documentos/5bbc69acb750603269e81f6e |
| Access Level: | Open access |
| Keyword: | Extension problem Fourier-Bessel expansions Heat equation Radial solutions Wave equation |
| Summary: | We study radial solutions of the Cauchy problem for the wave equation in the multidimensional unit ball Bd, d ≥ 1. In this case, the operator that appears is the Bessel Laplacian and the solution u (t, x) is given in terms of a Fourier-Bessel expansion. We prove that, for initial Lp data, the series converges in the L2 norm. The analysis of a particular operator, the adjoint of the Riesz transform for Fourier-Bessel series, is needed for our purposes, and may be of independent interest. As applications, certain Lp - L2 estimates for the solution of the heat equation and the extension problem for the fractional Bessel Laplacian are obtained. © 2013 Elsevier Ltd. All rights reserved. |
|---|