Shape optimization problems with Robin conditions on the free boundary
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 6, pp. 1539-1568.

We provide a free discontinuity approach to a class of shape optimization problems involving Robin conditions on the free boundary. More precisely, we identify a large family of domains on which such problems are well posed in a way that the extended problem can be considered a relaxed version of the corresponding one on regular domains, we prove existence of a solution and obtain some qualitative information on the optimal sets.

DOI : 10.1016/j.anihpc.2015.07.001
Mots-clés : Free boundary problems, Shape optimization problems, Robin boundary conditions, Free discontinuity problems, Functions of bounded variation 
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     author = {Bucur, Dorin and Giacomini, Alessandro},
     title = {Shape optimization problems with {Robin} conditions on the free boundary},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1539--1568},
     publisher = {Elsevier},
     volume = {33},
     number = {6},
     year = {2016},
     doi = {10.1016/j.anihpc.2015.07.001},
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     zbl = {1352.49045},
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     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2015.07.001/}
}
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Bucur, Dorin; Giacomini, Alessandro. Shape optimization problems with Robin conditions on the free boundary. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 6, pp. 1539-1568. doi : 10.1016/j.anihpc.2015.07.001. http://www.numdam.org/articles/10.1016/j.anihpc.2015.07.001/

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