Parabolic equations with measurable coefficients (Q884837)

The authors investigate the unique solvability of second order parabolic equations in non-divergence form \[ u_t+a^{jk}(t,x)u_{x^jx^k} +b^j(t,x)u_{x^j} +c(t,x)u=f \] in Sobolev spaces \(W^{1,2}_p((0,R)\times {\mathbb R}^d)\) with \(p\geq 2.\) The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables.