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Fractional calculus for power functions and eigenvalues of the fractional Laplacian

Author(s): Bartłlomiej Dyda

Publication date (Print): January 1 2012

Journal: Fractional Calculus and Applied Analysis

Publisher: Walter de Gruyter GmbH

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Abstract

We calculate the fractional Laplacian Δα/2 for functions of the form u(x) = (1 − |x|2)+p and v(x) = x d u(x). As an application, we estimate the first eigenvalues of the fractional Laplacian in a ball.

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Most cited references 21

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Foundations of Modern Potential Theory

N. S. Landkof (1972)

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Non-linear ground state representations and sharp Hardy inequalities

Rupert L. Frank, Robert Seiringer (2008)

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First passage times for symmetric stable processes in space

R. Getoor (1961)

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Author and article information

Journal

Title: Fractional Calculus and Applied Analysis

Publisher: Walter de Gruyter GmbH

ISSN (Electronic): 1314-2224

ISSN (Print): 1311-0454

Publication date Created: January 1 2012

Publication date (Print): January 1 2012

Volume: 15

Issue: 4

Article

DOI: 10.2478/s13540-012-0038-8

SO-VID: 204ebebe-4daf-4608-891e-f64d281099ad

Copyright © © 2012

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