Ricco, S., & Torricelli, A. (2024). A necessary condition for extremality of solutions to autonomous obstacle problems with general growth. Nonlinear Analysis: Real World Applications, 76, Article 104005. https://doi.org/10.1016/j.nonrwa.2023.104005
Obstacle problem; Characterization of solutions; Convex analysis; Variational inequality; General growth
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Abstract:
Let us consider an autonomous obstacle problem 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.
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Project title:
Smarte Materialien: Geometrie, Nichtlokalität, Chiralität: Y1292-N (FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) Nichtlokale Herausforderungen in der Kontinuumsmechanik: F 6513-N29 (FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
