The Harnack inequality for a class of nonlocal parabolic equations

DOI10.1142/S0219199720500509zbMath1469.35215arXiv1911.05619OpenAlexW3041576985MaRDI QIDQ5002180

Agnid Banerjee, Nicola Garofalo, Duy-Minh Nhieu, Isidro Humberto Munive

Publication date: 27 July 2021

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.05619

zbMATH Keywords

heat operatorextension problemscale invariant Harnack inequalityfractional powers of parabolic operators

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Second-order parabolic equations (35K10) Subelliptic equations (35H20) Fractional partial differential equations (35R11) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items

Regularity of solutions to the fractional Cheeger-Laplacian on domains in metric spaces of bounded geometry, Borderline gradient continuity for fractional heat type operators, Quantitative uniqueness for fractional heat type operators

Cites Work

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• Extension properties and boundary estimates for a fractional heat operator
• A new formulation of Harnack's inequality for nonlocal operators
• Fractional powers of closed operators and the semigroups generated by them
• A priori estimates for integro-differential operators with measurable kernels
• Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result
• Balls and metrics defined by vector fields. I: Basic properties
• A remark on a Harnack inequality for dengerate parabolic equations
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Monotonicity of generalized frequencies and the strong unique continuation property for fractional parabolic equations
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• A Saint-Venant type principle for Dirichlet forms on discontinuous media
• Fourier series, Fourier transform and their applications to mathematical physics
• Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
• Harnack inequality for fractional sub-Laplacians in Carnot groups
• Hypoelliptic second order differential equations
• THE HEAT EQUATION ON NONCOMPACT RIEMANNIAN MANIFOLDS
• Non-divergence equations structured on Hörmander vector fields: heat kernels and Harnack inequalities
• The local regularity of solutions of degenerate elliptic equations
• Poincare inequalities, isoperimetric estimates, and representation formulas on product spaces
• Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.
• The boundary Harnack principle for the fractional Laplacian
• Sobolev met Poincaré
• Some properties of sub-Laplaceans
• Fractional thoughts
• Regularity Theory and Extension Problem for Fractional Nonlocal Parabolic Equations and the Master Equation
• An Extension Problem Related to the Fractional Laplacian
• [https://portal.mardi4nfdi.de/wiki/Publication:5689214 Isoperimetric and Sobolev inequalities for Carnot-Carath�odory spaces and the existence of minimal surfaces]