The Evans-Krylov theorem for nonlocal fully nonlinear equations

2011/07/29 by Luis Caffarelli, Luis Silvestre, Luís Silvestre · 17 citations
Engineering · Computer Science · Mathematics · #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.4007/annals.2011.174.2.9

Abstract

We prove a regularity result for solutions of a purely integro-differential Bellman equation. This regularity is enough for the solutions to be understood in the classical sense. If we let the order of the equation approach two, we recover the theorem of Evans and Krylov about the regularity of solutions to concave uniformly elliptic partial differential equations.

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