Transference of fractional Laplacian regularity

  1. Roncal, L. 1
  2. Stinga, P.R. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 University of Texas at Austin
    info

    University of Texas at Austin

    Austin, Estados Unidos

    ROR https://ror.org/00hj54h04

Libro:
Special Functions, Partial Differential Equations, and Harmonic Analysis

ISBN: 9783319105444

Ano de publicación: 2014

Volume: 108

Páxinas: 203-212

Tipo: Capítulo de libro

DOI: 10.1007/978-3-319-10545-1_14 SCOPUS: 2-s2.0-84969228139 arXiv: 1406.6807 GOOGLE SCHOLAR lock_openAcceso aberto editor
Repositorio institucional: lockAcceso aberto Editor

Proxectos relacionados

Ortogonalidad y aproximación: teoría y aplicaciones en ciencia y tecnología

2013/00004/001

Resumo

In this note we show how to obtain regularity estimates for the fractional Laplacian on the multidimensional torus Tn from the fractional Laplacian on ℝn. Though at first glance this may seem quite natural, it must be carefully precised. A reason for that is the simple fact that L2functions on the torus cannot be identified with L2functions on ℝn. The transference is achieved through a formula that holds in the distributional sense. Such an identity allows us to transfer Harnack inequalities, to relate the extension problems, and to obtain pointwise formulas and Hölder regularity estimates. © Springer International Publishing Switzerland 2014.