On the smoothness of weak solutions of strong-nonlinear nondiagonal elliptic systems (the two-dimensional case)

We consider a class of strong-nonlinear elliptic systems with a nondiagonal principal matrix. Weak solvability of the Dirichlet problem for such type systems was earlier proved by the author in the two-dimensional case. The solution constructed was smooth almost everywhere. Here we prove that this solution is a Hölder continuous function in the entire domain.