Shape optimization problems with Robin conditions on the free boundary. (English) Zbl 1352.49045

Summary: 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.


49Q10 Optimization of shapes other than minimal surfaces
35R35 Free boundary problems for PDEs
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