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On a new Kato class and positive solutions of Dirichlet problems for the fractional Laplacian in bounded domains
Journal article   Peer reviewed

On a new Kato class and positive solutions of Dirichlet problems for the fractional Laplacian in bounded domains

Rym Chemmam, Habib Maagli and Syrine Masmoudi
Nonlinear analysis, Vol.74(5), pp.1555-1576
01/03/2011
DOI: https://doi.org/10.1016/j.na.2010.10.027

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
The purpose of this paper is to extend some results of the potential theory of an elliptic operator to the fractional Laplacian (-Delta)(a/2), 0 < alpha < 2, in a bounded C-1,C-1 domain D in R-n. In particular, we introduce a new Kato class K-alpha (D) and we exploit the properties of this class to study the existence of positive solutions of some Dirichlet problems for the fractional Laplacian. (C) 2010 Elsevier Ltd. All rights reserved.

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