SUBELLIPTIC VARIATIONAL-PROBLEMS

Using the direct method and the MOSER'S process, we prove the existence and C-mu regularity of stationary point for the degenerate elliptic variational problem I(mu) = integral-OMEGA F(x, u, Xu) dx where X = (X1,..., X(m)) is a system of real smooth vector fields which satisfy the Hormander's condition. The assumption imposed on F(x, u, xi) are similar to those for the elliptic case.