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

Abstract : 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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Cited literature [37 references]

https://hal.archives-ouvertes.fr/hal-00667276
Contributor : Tomasz Luks <>
Submitted on : Wednesday, March 14, 2012 - 2:13:04 PM
Last modification on : Monday, March 9, 2020 - 6:15:53 PM
Document(s) archivé(s) le : Friday, June 15, 2012 - 2:28:26 AM

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• HAL Id : hal-00667276, version 2

### Citation

Piotr Graczyk, Tomasz Jakubowski, Tomasz Luks. Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation. 2012. ⟨hal-00667276v2⟩

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