Smoothness of weak solutions of strongly-nonlinear nondiagonal elliptic systems (two-dimensional case)

Abstract

We consider a class of strongly-nonlinear elliptic systems with a nondiagonal principal matrix. The weak solvability of the Dirichlet problem for such systems has been earlier proved by the author in the two-dimensional case. It was shown that the solution constructed is smooth almost everywhere. In this paper, we prove that this solution is a Holder continuous function on the entire domain. Bibliography: 3 titles.