Hôlder continuity of solutions of second-order non-linear elliptic integro-differential equations

2010/09/03 by Guy Barles, Barles, Guy, Emmanuel Chasseigne +3 · 3 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.1009.0685

openalex publication_date 2010/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with Hölder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth conditions on the equation. These results are concerned with a large class of integro-differential operators whose singular measures depend on x and also a large class of equations, including Bellman-Isaacs Equations.

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• Qualitative properties of positive solutions to mixed local and nonlocal critical problems in ℝⁿ
• Regularity theory for degenerate fully nonlinear nonlocal equations with a Hamiltonian term
• Liouville results for (p,q)-Laplacian elliptic equations with source terms involving gradient nonlinearities

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