Applications of differential calculus to quasilinear elliptic boundary value problems with non-smooth data

This paper concerns boundary value problems for quasilinear second order elliptic systems which are, for example, of the type Here Ω is a Lipschitz domain in ν_j are the components of the unit outward normal vector field on ∂Ω, the sets Γ_β are open in ∂Ω and their relative boundaries are Lipschitz hypersurfaces in ∂Ω. The coefficient functions are supposed to be bounded and measurable with respect to the space variable and smooth with respect to the unknown vector function u and to the control parameter λ. It is shown that, under natural conditions, such boundary value problems generate smooth Fredholm maps between appropriate Sobolev-Campanato spaces, that the weak solutions are H?lder continuous up to the boundary and that the Implicit Function Theorem and the Newton Iteration Procedure are applicable.