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Research Article | Open Access

Some evaluations of the fractional p-Laplace operator on radial functions

Francesca Colasuonno1, Fausto Ferrari1( ), Paola Gervasio2, Alfio Quarteroni3,4
Dipartimento di Matematica, Alma Mater Studiorum Università di Bologna, piazza di Porta S. Donato, 5, 40126 Bologna, Italy
Dipartimento di Ingegneria Civile, Architettura, Territorio, Ambiente e di Matematica, Università degli Studi di Brescia, via Branze, 43, 25123 Brescia, Italy
MOX, Dipartimento di Matematica, Politecnico di Milano, via Bonardi, 9, 20133 Milano, Italy
EPFL Lausanne, Switzerland (Professor Emeritus)
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Abstract

We face a rigidity problem for the fractional p-Laplace operator to extend to this new framework some tools useful for the linear case. It is known that (−Δ)s(1−|x|2)+s and −Δp(1−|x|pp−1) are constant functions in (−1,1) for fixed p and s. We evaluated (−Δp)s(1−|x|pp−1)+s proving that it is not constant in (−1,1) for some p∈(1,+∞) and s∈(0,1). This conclusion is obtained numerically thanks to the use of very accurate Gaussian numerical quadrature formulas.

Keywords

fractional p-Laplacianstrong comparison principlep-fractional torsion problemGaussian quadrature formulasnumerical approximation of singular integrals
CLC number: 35B51, 35J99, 65D30

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Mathematics in Engineering
Volume 5 Issue 1,
February 2023
Pages 1-23
DOI: 10.3934/mine.2023015

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Cite this article:
Colasuonno F, Ferrari F, Gervasio P, et al. Some evaluations of the fractional p-Laplace operator on radial functions. Mathematics in Engineering, 2023, 5(1): 1-23. https://doi.org/10.3934/mine.2023015

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Received: 14 December 2021
Revised: 18 January 2022
Accepted: 18 January 2022
Published: 15 February 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)