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

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

2012-03-14

arxiv.org/abs/1203.3064v2

Mathematics

Analysis of PDEs

28 pages, editorial changes

Scientific paper

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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