Solvability of second-order equations with hierarchically partially BMO coefficients

Dong, Hongjie

doi:10.1090/S0002-9947-2011-05453-X

Solvability of second-order equations with hierarchically partially BMO coefficients
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Trans. Amer. Math. Soc. 364 (2012), 493-517 Request permission

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 to the full range of $p$, but also deal with equations with more general coefficients.

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