Green function estimates for relativistic stable processes in half-space-like open sets

DOI10.1016/j.spa.2011.01.004zbMath1235.60100OpenAlexW2151165919MaRDI QIDQ544510

Zhen-Qing Chen, Panki Kim, Renming Song

Publication date: 15 June 2011

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2011.01.004

zbMATH Keywords

Green functionexit timeLévy systemuniform Harnack inequalitysymmetric \(\alpha \)-stable processrelativistic stable processuniform boundary Harnack principle

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Markov semigroups and applications to diffusion processes (47D07) Transition functions, generators and resolvents (60J35) Integro-differential operators (47G20)

Related Items

Boundary behavior of \(\alpha \)-harmonic functions on the complement of the sphere and hyperplane ⋮ Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators ⋮ Dirichlet heat kernel estimates for \(\Delta ^{\alpha /2} + \delta ^{\beta /2}\) ⋮ Fractional nonlinear degenerate diffusion equations on bounded domains. I: Existence, uniqueness and upper bounds. ⋮ The Cauchy-Dirichlet problem for singular nonlocal diffusions on bounded domains ⋮ Sharp heat kernel estimates for relativistic stable processes in open sets ⋮ Global heat kernel estimates for relativistic stable processes in half-space-like open sets ⋮ Unique continuation properties for relativistic Schrödinger operators with a singular potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global heat kernel estimates for fractional Laplacians in unbounded open sets
• Sharp heat kernel estimates for relativistic stable processes in open sets
• Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions
• Potential theory of truncated stable processes
• Generalized 3G theorem and application to relativistic stable process on non-smooth open sets
• Hartree-Fock theory for pseudorelativistic atoms
• Heat kernel estimates for the Dirichlet fractional Laplacian
• Boundary Harnack principle for subordinate Brownian motions
• Relativistic stability of matter. I
• Spectral analysis of pseudodifferential operators
• Spectral theory of the operator \((p^2+m^2)^{1/2}-Ze^2/r\)
• The stability and instability of relativistic matter
• Drift transforms and Green function estimates for discontinuous processes
• Estimates of Green function for relativistic \(\alpha\)-stable process
• Boundary Harnack principle for symmetric stable processes
• Sharp estimates for the Green function in Lipschitz domains
• Two-sided optimal bounds for Green functions of half-spaces for relativistic \(\alpha\)-stable process
• Heat kernel estimates for jump processes of mixed types on metric measure spaces
• Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value
• Relative Fatou's theorem for (\(-\Delta)^{\alpha/2}\)-harmonic functions in bounded \(\kappa\)-fat open sets
• Heat kernel estimates for stable-like processes on \(d\)-sets.
• Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators
• Bessel potentials, hitting distributions and Green functions
• Intrinsic ultracontractivity of the Feynman-Kac semigroup for relativistic stable processes
• The large-Z Behavior of pseudorelativistic atoms
• The boundary Harnack principle for the fractional Laplacian
• Estimates on the Dirichlet heat kernel of domains above the graphs of bounded C1,1 functions
• On the Distribution of First Hits for the Symmetric Stable Processes