[L'inégalité de Harnack pour les processus symétriques stables sur les fractals]
Nous présentons l'inégalité de Harnack pour les fonctions α-harmoniques sur d-ensembles. En particulier cas de cellule naturelle du triangle de Sierpiński nous obtenons le principe de Harnack à la frontiére. Nous donnons aussi une estimation de la vitesse de decroissance des fonctions α-harmoniques près de la frontière ainsi que l'estimation de Carleson.
We study nonnegative harmonic functions of symmetric α-stable processes on d-sets F. We prove the Harnack inequality for such functions when α∈(0,2/dw)∪(ds,2). Furthermore, we investigate the decay rate of harmonic functions and the Carleson estimate near the boundary of a region in F. In the particular case of natural cells in the Sierpiński gasket we also prove the boundary Harnack principle.
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Krzysztof Bogdan 1 ; Andrzej Stós 1 ; Paweł Sztonyk 1
@article{CRMATH_2002__335_1_59_0,
author = {Krzysztof Bogdan and Andrzej St\'os and Pawe{\l} Sztonyk},
title = {Harnack inequality for symmetric stable processes on fractals},
journal = {Comptes Rendus. Math\'ematique},
pages = {59--63},
publisher = {Elsevier},
volume = {335},
number = {1},
year = {2002},
doi = {10.1016/S1631-073X(02)02425-1},
language = {en},
}
TY - JOUR AU - Krzysztof Bogdan AU - Andrzej Stós AU - Paweł Sztonyk TI - Harnack inequality for symmetric stable processes on fractals JO - Comptes Rendus. Mathématique PY - 2002 SP - 59 EP - 63 VL - 335 IS - 1 PB - Elsevier DO - 10.1016/S1631-073X(02)02425-1 LA - en ID - CRMATH_2002__335_1_59_0 ER -
Krzysztof Bogdan; Andrzej Stós; Paweł Sztonyk. Harnack inequality for symmetric stable processes on fractals. Comptes Rendus. Mathématique, Volume 335 (2002) no. 1, pp. 59-63. doi : 10.1016/S1631-073X(02)02425-1. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02425-1/
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