The first boundary value problem for nondivergence second order parabolic equations with discontinuous coefficients

This paper is concerned with the questions of solvability and smoothness of weak solutions of the first boundary value problem for a parabolic equation of the form
$$ \mathscr Lu=\sum^n_{i,k=1}a_{ik}(t,x)u_{x_ix_k}-u_t=f(t,x). $$

Bibliography: 18 titles.