2022/04/15 by D. Corona, A. Della Corte, Alessandro Della Corte +4
Computer Science · Engineering · Mathematics · Physics and Astronomy · #34B15 #49J45 #74B20 #74G35 #74G40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Beam (structure) #Bounded function #Contact Mechanics and Variational Inequalities #Elasticity and Wave Propagation #FOS: Mathematics #FOS: Physical sciences #Function (biology) #Geometry #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear system #Order (exchange) #Physics #Product (mathematics) #Pure mathematics #Quantum mechanics #Timoshenko beam theory #math-ph #math.AP #math.MP #msc:34B15 #msc:49J45 #msc:74B20 #msc:74G35 #msc:74G40
paper · pdf · doi:10.48550/arxiv.2204.07455
arxiv created 2022/04/15 · openalex publication_date 2022/04/15 · arxiv updated 2022/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the non-autonomous variational problem: inf(ϕ,θ) \∫01 ((k)/(2)ϕ'2 + ((ϕ-θ)2)/(2)-V(x,θ))dx\ where k>0, V is a bounded continuous function, (ϕ,θ)∈ H1([0,1])× L2([0,1]) and ϕ(0)=0 in the sense of traces. The peculiarity of the problem is its setting in the product of spaces of different regularity order. Problems with this form arise in elastostatics, when studying the equilibria of a nonlinear Timoshenko beam under distributed load, and in classical dynamics of coupled particles in time-depending external fields. We prove the existence and qualitative properties of global minimizers and study, under additional assumptions on V, the existence and regularity of local minimizers.