Positive solutions of nonlinear problems involving the square root of the Laplacian

Tan, Jinggang; Cabré, Xavier

doi:10.1016/j.aim.2010.01.025

Record: found
Abstract: not found
Article: not found

Positive solutions of nonlinear problems involving the square root of the Laplacian

Author(s): Xavier Cabré , Jinggang Tan

Publication date Created: August 2010

Publication date (Print): August 2010

Journal: Advances in Mathematics

Publisher: Elsevier BV

Read this article at

ScienceOpenPublisher

Bookmark

There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

Abstract

Related collections

Most cited references 15

Record: found
Abstract: found
Article: found

Is Open Access

An extension problem related to the fractional Laplacian

Luis A. Caffarelli, Luís Silvestre (2006)

The operator square root of the Laplacian \((-\lap)^{1/2}\) can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition. In this paper we obtain similar characterizations for general fractional powers of the Laplacian and other integro-differential operators. From those characterizations we derive some properties of these integro-differential equations from purely local arguments in the extension problems.