Parabolic equations with variably partially VMO coefficients (Q2892182)

The author studies the \( W^{1,2}_{p}\)-solvability, \(p\in(1,\infty)\), of second-order parabolic equations in nondivergence form NEWLINE\[NEWLINE -u_t+a^{ij}D_{ij}u + b^jD_ju+cu-\lambda u=f, \quad \lambda\geq 0, NEWLINE\]NEWLINE in the whole space. 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 direction allowed to depend on the cylinder. This extends a recent result by Krylov for elliptic equations.