Weighted Hessian estimates in Orlicz spaces for nondivergence elliptic operators with certain potentials

TL;DR

This paper establishes interior weighted Hessian estimates in Orlicz spaces for nondivergence elliptic equations with potentials satisfying reverse H"older conditions, advancing the understanding of regularity in such PDEs.

Contribution

It introduces new weighted Hessian estimates in Orlicz spaces for elliptic equations with specific potential conditions, extending previous regularity results.

Findings

Proved interior weighted Hessian estimates in Orlicz spaces.

Handled elliptic equations with potentials satisfying reverse H"older conditions.

Enhanced regularity theory for nondivergence elliptic operators.

Abstract

We prove interior weighted Hessian estimates in Orlicz spaces for nondivergence type elliptic equations with a lower order term which involves a nonnegative potential satisfying a reverse H\"older type condition.