Geodesic
Boundary potential theory for stable Lévy processes
Paweł Sztonyk1
1 Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
Colloquium Mathematicum, Tome 95 (2003) no. 2, pp. 191-206.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We investigate properties of harmonic functions of the symmetric stable Lévy process on ${\mathbb R}^{d}$ without the assumption that the process is rotation invariant. Our main goal is to prove the boundary Harnack principle for Lipschitz domains. To this end we improve the estimates for the Poisson kernel obtained in a previous work. We also investigate properties of harmonic functions of Feynman–Kac semigroups based on the stable process. In particular, we prove the continuity and the Harnack inequality for such functions.
DOI : 10.4064/cm95-2-4
Keywords: investigate properties harmonic functions symmetric stable process mathbb without assumption process rotation invariant main prove boundary harnack principle lipschitz domains end improve estimates poisson kernel obtained previous work investigate properties harmonic functions feynman kac semigroups based stable process particular prove continuity harnack inequality functions

Paweł Sztonyk 1

1 Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland 
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Paweł Sztonyk. Boundary potential theory for
 stable Lévy processes. Colloquium Mathematicum, Tome 95 (2003) no. 2, pp. 191-206. doi : 10.4064/cm95-2-4. http://geodesic.mathdoc.fr/articles/10.4064/cm95-2-4/

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