Geodesic
Shape Optimization Problems for Functionals with a Boundary Integral
Journal of convex analysis, Tome 28 (2021) no. 2, pp. 429-456
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We consider shape optimization problems for general integral functionals of the calculus of variations that may contain a boundary term. In particular, this class includes optimization problems governed by elliptic equations with a Robin condition on the free boundary. We show the existence of an optimal domain under rather general assumptions and we study the cases when the optimal domains are open sets and have a finite perimeter.
Classification : 49Q10, 49A15, 49A50, 35J20, 35D10
Mots-clés : Shape optimization, integral functionals, Robin condition, finite perimeter 
@article{JCA_2021_28_2_JCA_2021_28_2_a7,
     author = {G. Buttazzo and F. P. Maiale},
     title = {Shape {Optimization} {Problems} for {Functionals} with a {Boundary} {Integral}},
     journal = {Journal of convex analysis},
     pages = {429--456},
     year = {2021},
     volume = {28},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_2_JCA_2021_28_2_a7/}
}
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G. Buttazzo; F. P. Maiale. Shape Optimization Problems for Functionals with a Boundary Integral. Journal of convex analysis, Tome 28 (2021) no. 2, pp. 429-456. http://geodesic.mathdoc.fr/item/JCA_2021_28_2_JCA_2021_28_2_a7/