Oblique boundary value problems for equations of Monge-Ampère type (Q1389892)

The type of problem studied is \[ \text{det }D^2u= f(x,u,Du)\quad \text{in }\Omega,\quad D_\beta u+ \phi(x, u)=0\quad\text{on }\partial\Omega, \] where \(\Omega\) is a bounded uniformly convex domain and \(\beta\) a smooth oblique vector field. The author proves the existence of a unique solution under appropriate conditions.