Published Paper
Inserted: 26 may 2016
Last Updated: 26 may 2016
Journal: SIAM Control and Optimization
Volume: 48
Number: 5
Pages: 3003-3025
Year: 2009
Abstract:
In this paper, we focus on the following general shape optimization problem: \[ \min\{J(\Omega),\ \Omega\ convex,\ \Omega\in\mathcal S_{ad}\}, \] where $\mathcal S_{ad}$ is a set of 2-dimensional admissible shapes and $J:\mathcal{S}_{ad}\rightarrow\mathbb{R}$ is a shape functional. Using a specific parameterization of the set of convex domains, we derive some extremality conditions (first and second order) for this kind of problem. Moreover, we use these optimality conditions to prove that, for a large class of functionals (satisfying a concavity like property), any solution to this shape optimization problem is a polygon.
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