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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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Dates and versions

hal-00667276 , version 1 (07-02-2012)
hal-00667276 , version 2 (14-03-2012)

Identifiers

  • HAL Id : hal-00667276 , version 2

Cite

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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