Download PDF - Existence and uniqueness of solutions of the Darboux problem for the equation ${∂^3u \over ∂x_1 ∂x_2 ∂x_3} = {f(x_1, x_ 2, x_ 3, u, {∂u \over ∂x_1}, {∂u \over ∂x_2}, {∂u \over ∂x_3}, {∂^2u \over ∂x_1 ∂x_2}, {∂^2u \over ∂x_1, ∂x_3}, {∂^2u \over ∂x_2 ∂x_3})$