Symmetric Stable Processes in Cones

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Heat kernel estimates for the fractional Laplacian with Dirichlet conditions (2009, methodology): “The Martin kernel with the pole at infinity for D is sD(x) = δ D (x) [1].”
Estimates and structure of α-harmonic functions (2006, background): “pschitz (or even κ-fat) domain is thick at all its boundary points, as follows from [9] ([41]). For more information on the boundary potential theory in Lipschitz domains we refer to the papers [10], [4], [35], which may suggest further applications. We note that by Fatou’s lemma, if y ∈ ∂DM then PD”
Boundary Harnack inequality for Markov processes with jumps (2012, unknown): “Hölder continuity of harmonic functions is crucial in the theory of partial differential equations [6, 16], and the existence of limits of ratios of nonnegative harmonic functions leads to the construction of the Martin kernel and to representation of nonnegative harmonic functions ([5, 26]).”
On Kelvin Transformation (2006, background): “More compactly, (2) reads GTD(x, y)=KxKyGD(x, y), x, y ∈Rd 0 , (70) for every open D⊂Rd 0 .”
On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results (2016, background): “3 in [1] (see Section 3, and in particular Remark 3.”