Dirichlet problem for a class of second order nonlinear elliptic equations

Global existence and uniqueness of strong solutions to nonlinear elliptic partial differential equations are proved. The nonlinear operator under consideration is defined by Carath´eodory’s functions, and it is elliptic in sense of Campanato. The main tools of our investigations are both Leray–Schauder fixed point theorem and Aleksandrov–Pucci maximum principle.