Strong solvability for a class of nonlinear parabolic equations

Existence of strong solutions to Cauchy-Dirichlet problem for nonlinear parabolic equation is established. The nonlinear operator is prescribed by Carathéodory's function which satisfies an ellipticity condition due to S. Campanato. The main results are reached through Aleksandrov-Bakel'man-Pucci type maximum principle and topological fixed point theorem