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On the subordinate killed B.M in bounded domains and existence results for nonlinear fractional Dirichlet problems
Journal article   Peer reviewed

On the subordinate killed B.M in bounded domains and existence results for nonlinear fractional Dirichlet problems

Abdelwaheb Dhifli, Habib Maagli and Malek Zribi
Mathematische annalen, Vol.352(2), pp.259-291
01/02/2012
DOI: https://doi.org/10.1007/s00208-011-0642-7

Abstract

Mathematics Physical Sciences Science & Technology
We take up in this paper the existence of positive continuous solutions for some nonlinear boundary value problems with fractional differential equation based on the fractional Laplacian (-Delta(|D))(alpha/2) associated to the subordinate killed Brownian motion process ZDa in a boundedC1,1 domain D. Our arguments are based on potential theory tools on Z D a and properties of an appropriate Kato class of functions Ka( D).

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