On the Evans-Krylov theorem

TL;DR

This paper offers a shorter proof of the Evans-Krylov theorem, establishing interior regularity estimates for concave fully nonlinear elliptic equations, motivated by integral equations research.

Contribution

It presents a more concise proof of the Evans-Krylov theorem while maintaining the core techniques, advancing understanding of nonlinear elliptic PDE regularity.

Findings

Shorter proof of Evans-Krylov theorem

Maintains key tools of original proof

Provides insights for integral fully nonlinear equations

Abstract

In this note, motivated by our work on integral fully nonlinear equations, we provide a variation of the proof of Evans-Krylov theorem about the interior $C^{2,\alpha}$ a priori estimate for concave fully nonlinear elliptic equations. The proof we present is shorter compared to the original proofs, although the key tools used in the argument are the same.