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Journal of Convex Analysis 28 (2021), No. 2, 429--456
Copyright Heldermann Verlag 2021

Shape Optimization Problems for Functionals with a Boundary Integral

Giuseppe Buttazzo
Dip. di Matematica, UniversitÓ di Pisa, 56127 Pisa, Italy

Francesco Paolo Maiale
Scuola Normale Superiore, 56126 Pisa, Italy

We consider shape optimization problems for general integral functionals of the calculus of variations that may contain a boundary term. In particular, this class includes optimization problems governed by elliptic equations with a Robin condition on the free boundary. We show the existence of an optimal domain under rather general assumptions and we study the cases when the optimal domains are open sets and have a finite perimeter.

Keywords: Shape optimization, integral functionals, Robin condition, finite perimeter.

MSC: 49Q10, 49A15, 49A50, 35J20, 35D10.

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