Abstract

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.

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Keywords

  • Shape optimization
  • integral functionals
  • Robin condition
  • finite perimeter

Mathematics Subject Classification

49Q10, 49A15, 49A50, 35J20, 35D10

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Suggested citation

G. Buttazzo, F. P. Maiale. “Shape Optimization Problems for Functionals with a Boundary Integral.” Journal of Convex Analysis 28 (2021), No. 2, 429–456. https://doi.org/10.68381/jca28025

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press LLC.