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We present an existence theorem for a large class of nonlinearly elasticshells with low regularity in the framework of a two-dimensional theoryinvolving the mean and Gaussian curvatures. We restrict our discussion tohyperelastic materials, that is to elastic materials possessing a stored energyfunction. Under some specific conditions of polyconvexity, coerciveness andgrowth of the stored energy function, we prove the existence of globalminimizers. In addition, we define a general class of polyconvex stored energyfunctions which satisfies a coerciveness inequality.

Polyconvexity and Existence Theorem for Nonlinearly Elastic Shells