Schauder estimates for a class of fully nonlinear elliptic PDEs: a geometric tangential approach

Abstract

In this paper, we establish local and global Schauder estimates for classical solutions of a class of fully nonlinear elliptic partial differential equations, which are not necessarily convex or concave, under suitable Hölder continuity assumptions on the data. Our approach is based on a robust blow-up argument, combined with geometric tangential analysis and compactness techniques. This strategy is strongly influenced by methodologies developed in the contemporary theory of nonlinear elliptic PDEs.

arXiv commentPaper accepted in Annales Fennici Mathematici