# $C^{2,\alpha}$ estimates for solutions to almost linear elliptic equations

## TL;DR

This paper establishes $C^{2,eta}$ interior regularity estimates for viscosity solutions of nearly linear, fully non-linear elliptic equations, providing explicit bounds on how close the equations are to linear ones.

## Contribution

It introduces explicit bounds for the closeness of nearly linear elliptic equations to linear equations, enabling $C^{2,eta}$ regularity results for viscosity solutions.

## Key findings

- Proves $C^{2,eta}$ interior estimates for solutions.
- Provides explicit bounds on the closeness to linear equations.
- Extends regularity theory to nearly linear fully non-linear elliptic equations.

## Abstract

In this paper, we show $C^{2,\alpha}$ interior estimates for viscosity solutions of fully non-linear, uniformly elliptic equations, which are close to linear equations and we also compute an explicit bound for the closeness.