Title of article
On a new Kato class and positive solutions of Dirichlet problems for the fractional Laplacian in bounded domains Original Research Article
Author/Authors
Rym Chemmam، نويسنده , , Habib Maagli، نويسنده , , Syrine Masmoudi، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2011
Pages
22
From page
1555
To page
1576
Abstract
The purpose of this paper is to extend some results of the potential theory of an elliptic operator to the fractional Laplacian (−Δ)α/2(−Δ)α/2, 0<α<20<α<2, in a bounded C1,1C1,1 domain DD in RnRn. In particular, we introduce a new Kato class Kα(D)Kα(D) and we exploit the properties of this class to study the existence of positive solutions of some Dirichlet problems for the fractional Laplacian.
Keywords
Harmonic function , Martin representation , Fractional Laplacian , Green function , Symmetric stable process , Martin boundary , Dirichlet problem
Journal title
Nonlinear Analysis Theory, Methods & Applications
Serial Year
2011
Journal title
Nonlinear Analysis Theory, Methods & Applications
Record number
862997
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