Parabolic equations with variably partially VMO coefficients

Details Parabolic equations with variably partially VMO coefficients Parabolic equations with variably partially VMO coefficients

2008-11-25

arxiv.org/abs/0811.4124v1

Mathematics

Analysis of PDEs

17 pages, submitted for publication

Scientific paper

We prove the $W^{1,2}_{p}$-solvability of second order parabolic equations in nondivergence form in the whole space for $p\in (1,\infty)$. The leading coefficients are assumed to be measurable in one spatial direction and have vanishing mean oscillation (VMO) in the orthogonal directions and the time variable in each small parabolic cylinder with the direction depending on the cylinder. This extends a recent result by Krylov [17] for elliptic equations and removes the restriction that $p>2$.

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