2015/05/30 by Giuseppe Buttazzo, Buttazzo, Giuseppe, Edouard Oudet +4
Computer Science · Mathematics · #35J25 #35R35 #49J45 #49M05 #Advanced Mathematical Modeling in Engineering #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #math.OC #msc:35J25 #msc:35R35 #msc:49J45 #msc:49M05
paper · pdf · doi:10.48550/arxiv.1506.00141
29 pages, 42 figures
arxiv created 2015/05/30 · openalex publication_date 2015/05/30 · arxiv updated 2015/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A free boundary problem arising from the optimal reinforcement of a membrane or from the reduction of traffic congestion is considered; it is of the form sup∫Dθ dx=m infu∈ H10(D)∫D((1+θ)/(2)|∇ u|2-fu) dx. We prove the existence of an optimal reinforcement θ and that it has some higher integrability properties. We also provide some numerical computations for θ and u.