2018/01/27 by Behrouz Emamizadeh, Emamizadeh, Behrouz, Amin Farjudian +5
Chemistry · Computer Science · Mathematics · #35J20 #35J25 #65K10 #74H55 #Analysis of PDEs (math.AP) #Biochemistry #Chemistry #Computer science #Differential Equations and Numerical Methods #FOS: Mathematics #Mathematical analysis #Mathematical economics #Mathematical optimization #Mathematics #Membrane #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability (learning theory) #Uniqueness #math.AP #math.OC #msc:35J20 #msc:35J25 #msc:65K10 #msc:74H55
paper · pdf · doi:10.48550/arxiv.1801.09058
19 pages, 1 figure
arxiv created 2018/01/27 · openalex publication_date 2018/01/27 · arxiv updated 2018/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate a PDE-constrained optimization problem, with an intuitive interpretation in terms of the design of robust membranes made out of an arbitrary number of different materials. We prove existence and uniqueness of solutions for general smooth bounded domains, and derive a symmetry result for radial ones. We strengthen our analysis by proving that, for this particular problem, there are no non-global local optima. When the membrane is made out of two materials, the problem reduces to a shape optimization problem. We lay the preliminary foundation for computable analysis of this type of problem by proving stability of solutions with respect to some of the parameters involved.