Holder estimates for fully nonlinear integro-differential equations: Parabolic and nonlocal drift models

Héctor Chang Lara
UT Austin/Columbia University

We will revisit Holder estimates for some non local problems we worked recently with G. Davila. They arise in stochastic optimal control driven by purely jump processes. Each one of them can be considered as an extension of the Krylov-Safanov regularity theory for fully nonlinear second order equations. We will start by motivating these models and explaining what we considered as a nonlocal drift. Then we will see how the proofs work for very simple models and finally discuss how those ideas can be adapted to the nonlocal setting.