${\mathcal{C}}^{1,\gamma }$ regularity for singular or degenerate fully nonlinear operators and applications

Abstract

In this note, we prove ${\mathcal{C}}^{1,\gamma }$ regularity for solutions of some fully nonlinear degenerate elliptic equations with "superlinear" and "subquadratic " Hamiltonian terms. As an application, we complete the results of \cite{BDL1} concerning the associated ergodic problem, proving, among other facts, the uniqueness, up to constants, of the ergodic function.

14 pages, no figure