On problems in the calculus of variations in increasingly elongated domains

2017/05/03 by Hervé Le Dret, Dret, Hervé Le, Amira Mokrane +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · doi:10.48550/arxiv.1705.01466

openalex publication_date 2017/05/03 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We consider minimization problems in the calculus of variations set in a sequence of domains the size of which tends to infinity in certain directions and such that the data only depend on the coordinates in the directions that remain constant. We study the asymptotic behavior of minimizers in various situations and show that they converge in an appropriate sense toward minimizers of a related energy functional in the constant directions.

Related

• Optimal shapes for general integral functionals
• Miscellaneous applications of certain minimax theorems II
• On some Variational Problems set on domains tending to infinity
• Some monotonicity results for minimizers in the calculus of variations
• On a class of variational problems with linear growth and radial\n symmetry