Let us consider the autonomous obstacle problemmin(v) integral(Omega) F(Dv(x)) dxon 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. (c) 2023 Elsevier Ltd. All rights reserved.
A necessary condition for extremality of solutions to autonomous obstacle problems with general growth / Ricco, S.; Torricelli, A.. - In: NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS. - ISSN 1468-1218. - 76:(2024), pp. 1-16. [10.1016/j.nonrwa.2023.104005]
A necessary condition for extremality of solutions to autonomous obstacle problems with general growth
Torricelli A.
2024
Abstract
Let us consider the autonomous obstacle problemmin(v) integral(Omega) F(Dv(x)) dxon 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. (c) 2023 Elsevier Ltd. All rights reserved.
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