Consider a bounded domain $S\subset R^2$ and an elliptic system of two first order PDEs, namely a generalization of the Cauchy-Riemann system allowing nonconstant coefficients and lower order terms. Assume enough regularity for the coefficients to ensure Holder bounds. The coefficients depend on the solution itself, rendering the system quasilinear. I'm not imposing boundary conditions and I assume that there exists some solution.
Does the set of all solutions constitute a MANIFOLD in the corresponding Holder space, at least locally around the given solution? Which sort of manifold? Can anyone please suggest literature on this type of questions?