A Carleson type inequality for fully nonlinear elliptic equations with non-Lipschitz drift term

TL;DR

This paper extends boundary behavior analysis of solutions to fully nonlinear elliptic equations with non-Lipschitz drift, establishing a generalized Carleson estimate, boundary H"older continuity, and a boundary Harnack inequality.

Contribution

It introduces a generalized Carleson estimate for fully nonlinear elliptic equations with non-Lipschitz drift, expanding boundary regularity results.

Findings

Established a generalized Carleson estimate.

Proved boundary H"older continuity.

Derived a boundary Harnack inequality.

Abstract

This paper concerns the boundary behavior of solutions of certain fully nonlinear equations with a general drift term. We elaborate on the non-homogeneous generalized Harnack inequality proved by the second author in (Julin, ARMA -15), to prove a generalized Carleson estimate. We also prove boundary H\"older continuity and a boundary Harnack type inequality.