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.

28 pages, editorial changes