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

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 Hölder continuity and a boundary Harnack type inequality.

References in corpus (4)

• Equivalence of Viscosity and Weak Solutions for the $p(x)$-Laplacian
• Boundary Estimates for Certain Degenerate and Singular Parabolic Equations
• Generalized Harnack's inequality for nonhomogeneous elliptic equations
• Local bounds, Harnack inequality and Hölder continuity for divergence type elliptic equations with nonstardard growth