In this paper we survey some results on the Dirichlet problem \left{_u=g^Lu=f_inR^n\Ω^inΩ\
right. for nonlocal operators of the form Lu\left(x\right)=PVR^n\left{u\left(x\right) …

Density and tails of unimodal convolution semigroups - ScienceDirect Skip to main contentSkip
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This edited volume aims at giving an overview of recent advances in the theory and
applications of Partial Differential Equations and energy functionals related to the fractional …

We prove gradient estimates for harmonic functions with respect to a $ d $-dimensional
unimodal pure-jump Lévy process under some mild assumptions on the density of its Lévy …

We prove an optimal extension and trace theorem for Sobolev spaces of nonlocal operators.
The extension is given by a suitable Poisson integral and solves the corresponding nonlocal …

Dirichlet heat kernel for unimodal Lévy processes - ScienceDirect Skip to main contentSkip
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We consider a large class of symmetric pure jump Markov processes dominated by isotropic
unimodal Lévy processes with weak scaling conditions. First, we establish sharp two-sided …

We prove sharp boundary H {\" o} lder regularity for solutions to equations involving stable
integro-differential operators in bounded open sets satisfying the exterior $ C^{1,\text {dini}} …

In the first part of this article, we prove two-sided estimates of hitting probabilities of balls, the
potential kernel and the Green function for a ball for general isotropic unimodal Lévy …

We study the asymptotic formulas and estimates for the transition densities of isotropic
unimodal convolution semigroups of probability measures on under the assumption that its …