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.
@article{AIHPC_2016__33_6_1539_0, 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}, mrnumber = {3569242}, zbl = {1352.49045}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2015.07.001/} }
TY - JOUR AU - Bucur, Dorin AU - Giacomini, Alessandro TI - Shape optimization problems with Robin conditions on the free boundary JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 1539 EP - 1568 VL - 33 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2015.07.001/ DO - 10.1016/j.anihpc.2015.07.001 LA - en ID - AIHPC_2016__33_6_1539_0 ER -
%0 Journal Article %A Bucur, Dorin %A Giacomini, Alessandro %T Shape optimization problems with Robin conditions on the free boundary %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 1539-1568 %V 33 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2015.07.001/ %R 10.1016/j.anihpc.2015.07.001 %G en %F AIHPC_2016__33_6_1539_0
Bucur, Dorin; Giacomini, Alessandro. Shape optimization problems with Robin conditions on the free boundary. Annales de l'I.H.P. Analyse non linéaire, Volume 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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