Published Paper

Inserted: 28 mar 2025
Last Updated: 28 mar 2025

Journal: Nonlinear Anal. Real World Appl.
Year: 2024
Doi: 10.1016/j.nonrwa.2023.104005

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 find a necessary condition for the extremality of 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.

Keywords: obstacle problem, Variational inequality, general growth, convex analysis, Characterization of solutions