The wave equation for the Bessel Laplacian

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Ciaurri, Oscar¹  Roncal, Luz¹ 

[1] Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain

关键词: Wave equation;    Radial solutions;    Fourier-Bessel expansions;    Heat equation;    Extension problem;   

DOI  :  10.1016/j.jmaa.2013.06.039

来源: Elsevier

【 摘 要 】

We study radial solutions of the Cauchy problem for the wave equation in the multidimensional unit ball B-d, 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 L-p data, the series converges in the L-2 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 L-p - L-2 estimates for the solution of the heat equation and the extension problem for the fractional Bessel Laplacian are obtained. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free