  The paper considers parabolic equations in non-divergent form with
discontinuous coefficients at higher derivatives. Their investigation is most
complicated because, in general, in the case of discontinuous coefficients, the
uniqueness of a solution for nonlinear parabolic or elliptic equations can
fail, and there is no a priory estimate for partial derivatives of a solution.
In this paper, existence and regularity results are obtained under some Cordes
type restrictions on the coefficients. The results are applied to diffusion
processes.
