Solvability of second-order equations with hierarchically partially BMO coefficients

TL;DR

This paper investigates the solvability of second-order elliptic and parabolic equations with coefficients in locally BMO spaces, extending existing results to a broader range of p and more general coefficients.

Contribution

It extends previous solvability results to all p in (1,∞) for equations with hierarchically partially BMO coefficients, including more general coefficient conditions.

Findings

Established Lp-solvability for a full range of p

Extended results to more general coefficient classes

Built upon recent divergence form equation results

Abstract

By using some recent results for divergence form equations, we study the $L_p$-solvability of second-order elliptic and parabolic equations in nondivergence form for any $p\in (1,\infty)$. The leading coefficients are assumed to be in locally BMO spaces with suitably small BMO seminorms. We not only extend several previous results by Krylov and Kim [14]-[18] to the full range of $p$, but also deal with equations with more general coefficients.