Smoothness up to the boundary for solutions of the nonlinear and nonelliptic Dirichlet problem

Abstract:

For the Dirichlet problem associated with a general real second order p.d.e. $F(x, u, \nabla u, {\nabla ^2}u) = 0$ in a smooth open set $\Omega$ of ${{\mathbf {R}}^n}$, we prove smoothness up to the boundary of the solution $u$ for which the linearized characteristic form is nonnegative and satisfies Hörmander’s brackets condition, the boundary of $\Omega$ being noncharacteristic.