Fractional truncated Laplacians: representation formula, fundamental solutions and applications

DOI10.1007/s00030-022-00757-4zbMath1496.35420arXiv2010.02707OpenAlexW3091892114MaRDI QIDQ831424

Giulio Galise, Erwin Topp, Isabeau Birindelli

Publication date: 23 March 2022

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.02707

zbMATH Keywords

Liouville-type results

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Degenerate elliptic equations (35J70) Integral operators (47G10) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Inequalities involving derivatives and differential and integral operators (26D10) Positive solutions of integral equations (45M20) Fractional partial differential equations (35R11)

Related Items (4)

A family of nonlocal degenerate operators: maximum principles and related properties ⋮ Characterizations of the viscosity solution of a nonlocal and nonlinear equation induced by the fractional \(p\)-Laplace and the fractional \(p\)-convexity ⋮ Unnamed Item ⋮ Maximum principles and related problems for a class of nonlocal extremal operators

Cites Work

• Unnamed Item
• On the inequality \(F(x,D^2u)\geq f(u) +g(u)| Du|^q\)
• Hitchhiker's guide to the fractional Sobolev spaces
• Fundamental solutions and Liouville type theorems for nonlinear integral operators
• Second-order elliptic integro-differential equations: viscosity solutions' theory revisited
• On the Liouville property for fully nonlinear equations
• A family of degenerate elliptic operators: maximum principle and its consequences
• Viscosity solutions of nonlinear integro-differential equations
• On the strong maximum principle for second order nonlinear parabolic integro-differential equations
• Fractional convexity
• Games for eigenvalues of the Hessian and concave/convex envelopes
• Liouville theorems for a family of very degenerate elliptic nonlinear operators
• Some remarks on singular solutions of nonlinear elliptic equations. I
• Existence through convexity for the truncated Laplacians
• Integro-Differential equations with nonlinear directional dependence
• On Neumann type problems for nonlocal equations set in a half space
• Some Theorems on Stable Processes
• Dirichlet duality and the nonlinear Dirichlet problem
• Regularity theory for fully nonlinear integro-differential equations
• p-convexity, p-plurisubharmonicity, and the Levi problem
• An Extension Problem Related to the Fractional Laplacian
• On the Dirichlet problem for second-order elliptic integro-differential equations

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