Solvability of second-order equations with hierarchically partially BMO coefficients

Details Solvability of second-order equations with hierarchically partially BMO coefficients Solvability of second-order equations with hierarchically partially BMO coefficients

2010-09-28

arxiv.org/abs/1009.5657v1

Trans. Amer. Math. Soc. 364 (2012), 493-517

Mathematics

Analysis of PDEs

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

Scientific paper

10.1090/S0002-9947-2011-05453-X

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.

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