Interior $BMO$ regularity for elliptic equations in divergence form

TL;DR

This paper proves that weak solutions to certain elliptic equations in divergence form have interior BMO regularity, with assumptions on coefficients that are nearly optimal, advancing understanding of solution regularity.

Contribution

It establishes interior BMO regularity for solutions under nearly optimal coefficient conditions, improving previous regularity results for elliptic equations.

Findings

Solutions exhibit interior BMO regularity.

Coefficient assumptions are nearly optimal.

Enhances understanding of elliptic equation regularity.

Abstract

In this note, we establish the interior $BMO$ regularity of weak solutions to uniformly elliptic equations in divergence form. Moreover, the assumptions on the coefficients are nearly optimal.