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Let us consider the autonomous obstacle problem \begin{equation*} \min_v\int_\Omega F(Dv(x)) \, dx \end{equation*} on a specific class of admissiblefunctions, where we suppose the Lagrangian satisfies proper hypotheses ofconvexity and superlinearity at infinity. Our aim is to characterize thesolution, which exists and it is unique, thanks to a primal-dual formulation ofthe problem. The proof is based on classical arguments of Convex Analysis andon Calculus of Variations' techniques.

A necessary condition for extremality of solutions to autonomous obstacle problems with general growth