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Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators.
In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli and Silvestre and a class of conformally covariant operators in conformal...
Abstract: For $\alpha \in (1,2)$ we consider the equation $\partial_t u = \Delta^{\alpha/2} u - r b \cdot \nabla u$, where $b$ is a divergence free singular vector field not necessarily belonging to t...
Suppose $d\geq 2$ and $\alpha \in (1, 2)$. Let $D$ be a bounded $C^{1,1}$ open set in $R^d$ and $b$ an $R^d$-valued function on $R^d$ whose components are in a certain Kato class of the rotationally ...
Motivated by the "tug-of-war" game studied in [12], we consider a "non-local" version of the game which goes as follows: at every step two players pick respectively a direction and then, instead of f...
The Green function of the fractional Laplacian of the differential order bigger than one and the Green function of its gradient perturba-tions are comparable for bounded smooth multidimensional open s...
A Berezin-Li-Yau type inequality for (−) /2|, the fractional Laplacian op-erators restriced to a bounded domain ⊂ Rd for ∈ (0, 2], d ≥ 2, has not been known so far. First we positivel...
The fractional Laplacian (−△)/2 commutes with the primary coordination transformations in the Euclidean space Rd: dilation, translation and rotation.

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