JournalsaihpcVol. 33, No. 6pp. 1539–1568

Shape optimization problems with Robin conditions on the free boundary

  • Dorin Bucur

    Laboratoire de Mathématiques, CNRS UMR 5127 Université de Savoie & Institut Universitaire de France, Campus Scientifique, 73376 Le-Bourget-Du-Lac, France

  • Alessandro Giacomini

    DICATAM, Sezione di Matematica, Università degli Studi di Brescia, Via Valotti 9, 25133 Brescia, Italy
Shape optimization problems with Robin conditions on the free boundary cover
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Abstract

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.

Cite this article

Dorin Bucur, Alessandro Giacomini, Shape optimization problems with Robin conditions on the free boundary. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 6, pp. 1539–1568

DOI 10.1016/J.ANIHPC.2015.07.001