Regularity for the supercritical fractional Laplacian with drift

DOI10.1007/s12220-015-9590-xzbMath1375.35598arXiv1309.5892OpenAlexW2082574182MaRDI QIDQ282820

Camelia A. Pop, Charles L. Epstein

Publication date: 12 May 2016

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.5892

zbMATH Keywords

Sobolev spacesMarkov processespseudo-differential operatorsjump diffusion processesfractional Laplaciansymmetric stable processes

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Smoothness and regularity of solutions to PDEs (35B65) Pseudodifferential operators as generalizations of partial differential operators (35S05) Nonlinear elliptic equations (35J60) Second-order elliptic equations (35J15) Fractional partial differential equations (35R11)

Related Items (8)

Well-posedness for a class of pseudodifferential diffusion equations on the torus ⋮ The obstacle problem for the fractional Laplacian with critical drift ⋮ On positive supersolutions of fractional elliptic equations with gradient terms ⋮ On the well-posedness for a class of pseudo-differential parabolic equations ⋮ Fractional thoughts ⋮ Drift diffusion equations with fractional diffusion on compact Lie groups ⋮ Hölder estimates for nonlocal-diffusion equations with drifts ⋮ High Order Conservative Finite Difference/Fourier Spectral Methods for Inviscid Surface Quasi-Geostrophic Flows

Cites Work

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• Estimates of the Green function for the fractional Laplacian perturbed by gradient
• Time-dependent gradient perturbations of fractional Laplacian
• Optimal regularity of solutions to the obstacle problem for the fractional Laplacian with drift
• Nonlocal maximum principles for active scalars
• Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation
• The analysis of linear partial differential operators. III: Pseudo-differential operators
• Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation
• Eventual regularization of the slightly supercritical fractional Burgers equation
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Partial differential equations. I: Basic theory
• Partial differential equations. II: Qualitative studies of linear equations
• Variation on a theme of Caffarelli and Vasseur
• Estimates of heat kernel of fractional Laplacian perturbed by gradient operators
• Fractional Laplacian with singular drift
• Behavior of Solutions of 2D Quasi-Geostrophic Equations
• Hölder estimates for advection fractional-diffusion equations
• On the differentiability of the solution to an equation with drift and fractional diffusion

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