Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation

Let $L=\Delta^{\alpha/2}+ b\cdot\nabla$ with $\alpha\in(1,2)$. We prove the Martin representation and the Relative Fatou Theorem for non-negative singular $L$-harmonic functions on ${\mathcal C}^{1,1}$ bounded open sets.

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Source https://hal.science/hal-00667276
Author Graczyk, Piotr, Jakubowski, Tomasz, Luks, Tomasz
Maintainer CCSD
Last Updated May 24, 2026, 18:51 (UTC)
Created May 24, 2026, 18:51 (UTC)
Identifier hal-00667276
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Laboratoire Angevin de Recherche en Mathématiques (LAREMA) ; Université d'Angers (UA)-Centre National de la Recherche Scientifique (CNRS)
creator Graczyk, Piotr
date 2012-03-14T00:00:00
harvest_object_id a17ce166-c7ab-4f88-bf36-3008ef3a7a07
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2026-02-23T00:00:00
set_spec type:UNDEFINED