# $W^{2,p}$ interior estimates of fully nonlinear elliptic equations

## TL;DR

This paper extends $W^{2,p}$ interior estimates for fully nonlinear elliptic equations by relaxing coefficient regularity conditions and broadening the range of $p$, enhancing the applicability of these estimates.

## Contribution

It generalizes previous $W^{2,p}$ estimates by reducing regularity assumptions on coefficients and expanding the range of $p$ for which estimates hold.

## Key findings

- Relaxed regularity conditions on coefficients.
- Broadened the valid range of $p$ in estimates.
- Enhanced applicability of interior regularity results.

## Abstract

In this paper, we generalize the $W^{2,p}$ interior estimates of fully nonlinear elliptic equations that were obtained by Caffarelli in [1]. The generalizations are carried out in two directions. One is that we relax the regularity requirement on the "constant coefficients" equations and the other one is that we broaden the range of $p$.