Relaxation for an optimal design problem in BD(Ω)

2021/11/11 by Ana Cristina Barroso, Barroso, Ana Cristina, José Matías +3
Computer Science · Mathematics · #49J45 #49Q10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2111.06287

openalex publication_date 2021/11/11 · openalex created_date 2023/03/20 · openalex updated_date 2026/07/28

Abstract

We obtain a measure representation for a functional arising in the context of optimal design problems under linear growth conditions. The functional in question corresponds to the relaxation with respect to a pair (χ,u), where χ is the characteristic function of a set of finite perimeter and u is a function of bounded deformation, of an energy with a bulk term depending on the symmetrised gradient as well as a perimeter term.

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