Solvability of second-order equations with hierarchically partially BMO coefficients

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.

28 Pages. An earlier version was submitted in 2009. The current version is to appear in Trans. Amer. Math. Soc

References in corpus (1)

• Elliptic equations in divergence form with partially BMO coefficients

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