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Nonlinear oblique boundary value problems for two dimensional Hessian and curvature equations

where A ( D2u) denotes the vector of eigenvalues of the Hessian D2u of a C 2 real valued function u and f is a smooth real valued symmetric function defined on a region I; C lR n. Equations of this type arise in many situations. In differential geometry Hessian equations arise in connection with the Minkowski, Christoffel and similar problems (see [16]). Typical examples are Poisson's equation (3) b.u = g' and the Monge-Ampere equation