Interior regularity for strong solutions to a class of fully nonlinear elliptic equations

TL;DR

This paper establishes local second derivative estimates for strong solutions to certain fully nonlinear elliptic equations, advancing understanding in geometric analysis and PDE regularity theory.

Contribution

It provides new local regularity results for $W^{2,p}$-strong solutions to a class of fully nonlinear elliptic equations, inspired by conformal geometry problems.

Findings

Established local pointwise second derivative estimates

Extended regularity theory for fully nonlinear elliptic equations

Applied results to problems in conformal geometry

Abstract

We obtain local pointwise second derivative estimates for $W^{2,p}$-strong solutions to a class of fully nonlinear elliptic equations on Euclidean domains, motivated by problems in conformal geometry.