Geodesic
Occupational measures and averaged shape optimization
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 1141-1165

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We consider the minimization of averaged shape optimization problems over the class of sets of finite perimeter. We use occupational measures, which are probability measures defined in terms of the reduced boundary of sets of finite perimeter, that allow to transform the minimization into a linear problem on a set of measures. The averaged nature of the problem allows the optimal value to be approximated with sets with unbounded perimeter. In this case, we show that we can also approximate the optimal value with convex polytopes with n+1 faces shrinking to a point. We derive conditions under which we show the existence of minimizers and we also analyze the appropriate spaces in which to study the problem.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2017017
Classification : 49Q20, 49Q10, 28A33
Keywords: Shape optimization, occupational measures, sets of finite perimeter, Cheeger sets

Bright, Ido 1 ; Li, Qinfeng 1 ; Torres, Monica 1

1 
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     title = {Occupational measures and averaged shape optimization},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1141--1165},
     publisher = {EDP-Sciences},
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     year = {2018},
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Bright, Ido; Li, Qinfeng; Torres, Monica. Occupational measures and averaged shape optimization. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 1141-1165. doi: 10.1051/cocv/2017017

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