hi,

does anyone know some good references (books, papers) on partial differential equations with mixed boundary conditions ?

actually I am intrested in the following: Let $f(x)=(f_{1}(x),...,f_{n}(x))$ such that $x \in \mathbb{R}^{n}$ be an unknown function and denote by $J(f)$ the Jacobian of $f$. There is a first order partial non-linear equation, where $f$ is the unknown function, i.e. $F(J(f)(x),f(x),x)=g(x)$ (where one can assume that $F$ is "nice" and $g$ is some given "nice" function) on a domain $D$ in $\mathbb{R}^{n}$ such that $\partial D=C_{1} \cup C_{2}$. And the boundary conditions are: $f$ restricted to $C_{1}$ is zero and $J(f)$ restricted to $C_{2}$ is zero (as a matrix). Are there some references on such kind of equations ?

Does anyone have an idea, about some references or this is to be solved ???

pascal