Uniqueness for second-order parabolic equations with discontinuous coefficients

We prove uniqueness of the good solution to the Cauchy–Dirichlet (C–D) problem for linear non-variational parabolic equations with the coefficients of the principal part with discountinuities, in cases in which in general uniqueness of strong solutions in Sobolev spaces does not hold. In particular, we prove uniqueness when the discontinuities of the coefficients are contained in a hyperplane t = t0 and, with an extra condition on the eigenvalues of the matrix, in a line segment x = x0.