2013/11/02 by Ido Bright, Bright, Ido
Computer Science · Mathematics · #49J15 #49N20 #49Q10 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.OC #msc:49J15 #msc:49N20 #msc:49Q10
paper · pdf · doi:10.48550/arxiv.1311.0328
arxiv created 2013/11/02 · openalex publication_date 2013/11/02 · arxiv updated 2013/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish a PoincarÈ-Bendixson type result for a weighted averaged infinite horizon problem in the plane, with and without averaged constraints. For the unconstrained problem, we establish the existence of a periodic optimal solution, and for constrained problem, we establish the existence of an optimal solution that alternates cyclicly between a finite number of periodic curves, depending on the number of constraints. Applications of these results are presented to the shape optimization problems of the Cheeger set and the generalized Cheeger set, and also to a singular limit of the one-dimensional Cahn-Hilliard equation