  We present an existence theorem for a large class of nonlinearly elastic
shells with low regularity in the framework of a two-dimensional theory
involving the mean and Gaussian curvatures. We restrict our discussion to
hyperelastic materials, that is to elastic materials possessing a stored energy
function. Under some specific conditions of polyconvexity, coerciveness and
growth of the stored energy function, we prove the existence of global
minimizers. In addition, we define a general class of polyconvex stored energy
functions which satisfies a coerciveness inequality.
