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Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators
Harmonic function boundary Harnack principle gradient estimate
2016/1/20
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators.
Fractional Laplacian in conformal geometry
Conformal geometry Fractional Laplacian Conformally covariant operators Dirichlet-to-Neumann operators Asymptotically hyperbolic manifolds
2014/4/3
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...
Fractional Laplacian with singular drift
fractional Laplacian gradient perturbations singular drift
2011/9/13
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...
Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation
Dirichlet heat kernel fractional Laplacian gradient perturbation
2010/11/19
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 ...
Non-Local Tug-of-War and the Infinity Fractional Laplacian
Non-Local Tug-of-War the Infinity Fractional Laplacian
2010/11/15
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...
Estimates of the Green function for the fractional Laplacian perturbed by gradient
Estimates of the Green function fractional Laplacian
2010/12/6
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 the fractional Laplacian on a bounded domain
Berezin-Li-Yau type inequality fractional Laplacian bounded domain
2010/12/9
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...
Left-Inverses of Fractional Laplacian and Sparse Stochastic Processes
Left-Inverses of Fractional Laplacian Sparse Stochastic Processes
2010/12/6
The fractional Laplacian (−△)/2 commutes with the primary coordination transformations in the Euclidean space Rd: dilation, translation and rotation.