Fully nonlinear integro-differential equations with deforming kernels
Fully nonlinear integro-differential equations with deforming kernels
We develop a regularity theory for integro-differential equations with kernels deforming in space like sections of a convex solution of a Monge–Ampère equation. We prove an ABP estimate and a Harnack inequality, and derive Hölder and C1,α regularity results for solutions.