Inserted: 15 jan 2015
Last Updated: 9 mar 2016
Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
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.