# Solvability of second-order equations with hierarchically partially BMO coefficients - Mathematics > Analysis of PDEs

Abstract: By using some recent results for divergence form equations, we study the$L p$-solvability of second-order elliptic and parabolic equations innondivergence form for any $p\in 1,\infty$. The leading coefficients areassumed to be in locally BMO spaces with suitably small BMO seminorms. We notonly extend several previous results by Krylov and Kim 14-18 to the fullrange of $p$, but also deal with equations with more general coefficients.

Author: Hongjie Dong

Source: https://arxiv.org/