@article{Boulkhemair2023, 
author = {Abdesslam Boulkhemair and Abdelkrim Chakib and Azeddine Sadik},
title = {On a shape derivative formula for star-shaped domains using Minkowski deformation},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {8},
pages = {19773-19793},
keywords = {shape optimization, gauge function, shape derivative, volume functional, convex domain, star-shaped domain, support function, Minkowski deformation, Brunn-Minkowski theory},
url = {https://www.sciopen.com/article/10.3934/math.20231008},
doi = {10.3934/math.20231008},
abstract = {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.}
}