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

    GRID grid.119021.a

Journal:
Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Year of publication: 2014

Volume: 1

Issue: 1

Pages: 263-274

Type: Article

Export: RIS
DOI: 10.1016/j.jmaa.2013.06.039 SCOPUS: 2-s2.0-84883463453 WoS: 000324974700025 GOOGLE SCHOLAR
Institutional repository: lock_openOpen access editor

Metrics

Cited by

  • Scopus Cited by: 0 (12-06-2021)

Journal Citation Reports

  • Year 2014
  • Journal Impact Factor: 1.12
  • Best Quartile: Q1
  • Area: MATHEMATICS Quartile: Q1 Rank in area: 40/312 (Ranking edition: SCIE)
  • Area: MATHEMATICS, APPLIED Quartile: Q2 Rank in area: 74/257 (Ranking edition: SCIE)

SCImago Journal Rank

  • Year 2014
  • SJR Journal Impact: 1.295
  • Best Quartile: Q1
  • Area: Analysis Quartile: Q1 Rank in area: 29/130
  • Area: Applied Mathematics Quartile: Q1 Rank in area: 81/574

CiteScore

  • Year 2014
  • CiteScore of the Journal : 2.1
  • Area: Analysis Percentile: 75
  • Area: Applied Mathematics Percentile: 64

Abstract

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.