Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces

TL;DR

This paper establishes weighted and mixed-norm Sobolev estimates for fully nonlinear elliptic and parabolic equations in the entire space, under relaxed convexity and almost VMO conditions, including interior and boundary estimates.

Contribution

It introduces new Sobolev estimates for nonlinear PDEs with relaxed convexity and VMO conditions, extending previous regularity results.

Findings

Weighted Sobolev estimates proved for nonlinear elliptic and parabolic equations

Mixed-norm estimates established in whole space

Interior and boundary estimates obtained

Abstract

We prove weighted and mixed-norm Sobolev estimates for fully nonlinear elliptic and parabolic equations in the whole space under a relaxed convexity condition with almost VMO dependence on space-time variables. The corresponding interior and boundary estimates are also obtained.