Smoothness up to the Boundary for Solutions of the Nonlinear and Nonelliptic Dirichlet Problem
C. J. Xu, C. Zuily · Transactions of the American Mathematical Society · 1988
For the Dirichlet problem associated with a general real second order p.d.e. $F(x, u, abla u, { abla ^2}u) = 0$ 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.