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arXiv · 2204.05347

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

Samuele Riccò·Andrea Torricelli
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Abstract

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

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Samuele Riccò, Andrea Torricelli. 2022-04-11. A necessary condition for extremality of solutions to autonomous obstacle problems with general growth. https://arxiv.org/abs/2204.05347

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