Regularity for a class of nonlinear elliptic systems,

In this article we demonstrate that the solutions of a certain class of non-linear elliptic systems are smooth in the interior of the domain. One example of this class of equations is the system We shall prove regularity in the interior for solutions of systems which do not depend explicitly on either the independent variable or the functions, but only on the derivatives of the functions. An extension to a more general class of systems of the same type with smooth dependence on dependent and independent variables will be important for integrals which arise in Riemannian geometry and probably can be carried out without any radically different techniques. Homogeneous Dirichlet and Neumann boundary value problems may be treated by reflection; however, the regularity up to the boundary for (1) Research supported under National Science Foundation contract MPS73-08821 A02