Work

An Extension Problem Related to the Fractional Laplacian

Year: 2007

Type: article

Abstract: The operator square root of the Laplacian (− ▵)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 article, 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.

Source: Communications in Partial Differential Equations

DOI: 10.1080/03605300600987306

Authors: Luis Caffarelli, Luis Silvestre

Institutions: The University of Texas at Austin, Courant Institute of Mathematical Sciences

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

OpenAlex ID: W2172034033