Harnck inequalities and H\"older estimates for fully nonlinear integro-differential equations with weak scaling conditions

TL;DR

This paper establishes H"older estimates and Harnack inequalities for fully nonlinear integro-differential equations with variable order kernels near 2, under mild assumptions, expanding the understanding of their regularity properties.

Contribution

It introduces new regularity results for nonlinear integro-differential equations with variable order kernels close to 2, under weak scaling conditions.

Findings

Proved H"older continuity for solutions.

Established Harnack inequalities under mild assumptions.

Extended results to kernels of variable order near 2.

Abstract

H\"older estimates and Harnack inequalities are studied for fully nonlinear integro-differential equations under some mild assumptions. We allow the kernels of variable order and critically close to 2.