The wave equation for the Bessel Laplacian

  1. Ciaurri, T. 1
  2. Roncal, L. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Año de publicación: 2014

Volumen: 1

Número: 1

Páginas: 263-274

Tipo: Artículo

DOI: 10.1016/J.JMAA.2013.06.039 SCOPUS: 2-s2.0-84883463453 WoS: WOS:000324974700025 GOOGLE SCHOLAR

Otras publicaciones en: Journal of Mathematical Analysis and Applications

Resumen

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.