Quasilinear Cauchy-Dirichlet problem for parabolic equations with $VMO_x$ coefficients

We study the strong solvability of the Cauchy-Dirichlet problem for parabolic quasilinear equations with discontinuous data. The principal coefficients depend on the point $(x, t)$ and on the solution u, the dependence on $x$ is of $VMO$ type while these are only measurable with respect to $t$. Assuming suitable structural conditions on the nonlinear terms, we prove existence and uniqueness of the strong solution, which turns out to be also Hölder continuous.