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A result concerning global extrema in a nonsmooth nonconvex variationalproblem that appears in applications (e.g. in a large deformation elasticityproblem) is investigated in comparison with a result of D.Y. Gao and R.W.Ogden. The tools used are elementary and the results derived improve upon andcorrect a recent similar result, more precisely, Theorem 4 of the paper"Closed-form solutions, extremality and nonsmoothness criteria in a largedeformation elasticity problem" by the fore-mentioned authors.

A non-convex variational problem appearing in a large deformation elasticity problem