A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications

Zhenyu Fan

paper

A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications

arXiv:2509.01138

Abstract

In this note, we generalize Savin's small perturbation theorem to nonhomogeneous fully nonlinear equations $F (D^{2} u, D u, u, x) = f$ provided the coefficients and the right-hand side terms are Hölder small perturbations. As an application, we establish a partial regularity result for the sigma- $k$ Hessian equation $σ_{k} (D^{2} u) = f$ .

arXiv comment25 pages