The Dirichlet problem for stable-like operators and related probabilistic representations

DOI10.1080/03605302.2016.1207084zbMath1352.60080OpenAlexW2467268925WikidataQ60167475 ScholiaQ60167475MaRDI QIDQ2833304

Luis A. Caffarelli, Anup Biswas, Aristotle Arapostathis

Publication date: 17 November 2016

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2016.1207084

zbMATH Keywords

Dirichlet problemjumpsHarnack inequalitystochastic differential equationsexit timepositive recurrence\(\alpha\)-stable processinvariant probability measure

Mathematics Subject Classification ID

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Cites Work

• Schauder estimates for solutions of linear parabolic integro-differential equations
• Non-local gradient dependent operators
• Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations
• Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation
• Regularity results for nonlocal equations by approximation
• Regularity results for stable-like operators
• Criteria for ergodicity of Lévy type operators in dimension one
• Stochastic differential equations with jumps
• The martingale problem for a class of stable-like processes
• Harnack inequality for some classes of Markov processes
• Stability for multidimensional jump-diffusion processes
• Harnack inequalities for jump processes
• Harnack's inequality for stable Lévy processes
• Analysis of jump processes with nondegenerate jumping kernels
• Regularity for solutions of nonlocal, nonsymmetric equations
• Harmonic functions for a class of integro-differential operators
• The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
• Weak and viscosity solutions of the fractional Laplace equation
• Estimates of heat kernel of fractional Laplacian perturbed by gradient operators
• Uniqueness of stable processes with drift
• Equivalence of Stochastic Equations and Martingale Problems
• Ergodic Control of Diffusion Processes
• Nonlocal Operators with Applications to Image Processing
• Non-local Dirichlet forms and symmetric jump processes
• Regularity theory for fully nonlinear integro-differential equations
• Lévy Processes and Stochastic Calculus
• Elliptic Partial Differential Equations of Second Order
• Financial Modelling with Jump Processes
• Harnack inequalities for non-local operators of variable order
• On the Dirichlet problem for second-order elliptic integro-differential equations
• Harnack inequality for some discontinuous Markov processes with a diffusion part
• Hölder Continuity of Harmonic Functions with Respect to Operators of Variable Order
• C^{1, α}Interior Regularity for Nonlinear Nonlocal Elliptic Equations with Rough Kernels

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