A Quasilinear Cauchy-Dirichlet Problem for Parabolic Equations with VMOx Coefficients

The strong solvability of the Cauchy-Dirichlet problem for parabolic quasilinear equations with discontinuous data is investigated. The leading coefficients depend on the point (x, t) and on the solution u, the dependence on x is of the VMO type, while with respect to t only measurability is required from them. Under suitable structural conditions on the nonlinear terms, the existence and uniqueness of a strong solution is proved, which also turns out to be Hölder continuous.