On a shape derivative formula for star-shaped domains using Minkowski deformation-Reference-Cited by-同舟云学术

On a shape derivative formula for star-shaped domains using Minkowski deformation

Published:2023 Issue:8 Volume:8 Page:19773-19793
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Boulkhemair Abdesslam¹,Chakib Abdelkrim²,Sadik Azeddine¹²

Affiliation:

1. Laboratoire de Mathématiques Jean Leray, UMR6629 CNRS, UFR Sciences et Techniques, 2 rue de la Houssinière, BP92208, 44322 Nantes, France

2. Applied Mathematics Team, Faculty of Sciences and Techniques, Sultan Moulay Slimane University, Beni Mellal, Morocco

Abstract

<abstract><p>We consider the shape derivative formula for a volume cost functional studied in previous papers where we used the Minkowski deformation and support functions in the convex setting. In this work, we extend it to some non-convex domains, namely the star-shaped ones. The formula happens to be also an extension of a well-known one in the geometric Brunn-Minkowski theory of convex bodies. At the end, we illustrate the formula by applying it to some model shape optimization problem.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference22 articles.

1. G. Allaire, Conception optimale de structures, Berlin: Springer, 2007. http://dx.doi.org/10.1007/978-3-540-36856-4

2. A. Boulkhemair, On a shape derivative formula in the Brunn-Minkowski theory, SIAM J. Control Optim., 55 (2017), 156–171. http://dx.doi.org/10.1137/15M1015844

3. A. Boulkhemair, A. Chakib, On a shape derivative formula with respect to convex domains, J. Convex Anal., 21 (2014), 67–87.

4. A. Boulkhemair, A. Chakib, Erratum: on a shape derivative formula with respect to convex domains, J. Convex Anal., 22 (2015), 901–903.

5. A. Boulkhemair, A. Chakib, A. Nachaoui, A. Niftiyev, A. Sadik, On a numerical shape optimal design approach for a class of free boundary problems, Comput. Optim. Appl., 77 (2020), 509–537. http://dx.doi.org/10.1007/s10589-020-00212-z

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Differentiation with Respect to Domains of Boundary Integral Functionals Involving Support Functions;Applied Mathematics & Optimization;2024-07-29