Interfaces and Free Boundaries


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Volume 9, Issue 1, 2007, pp. 133–148
DOI: 10.4171/IFB/159

Published online: 2007-03-31

Uniqueness, symmetry and full regularity of free boundary in optimization problems with volume constraint

Eduardo V. Teixeira[1]

(1) Universidade Federal do CearĂ¡, Fortaleza, Brazil

In this paper we study qualitative geometric properties of optimal configurations to a variational problem with free boundary, under suitable assumptions on a fixed boundary. More specifically, we study the problem of minimizing the flow of heat given by $\int_{\partial D} \Gamma (u_\mu) d\sigma$, where $D$ is a fixed domain and $u$ is the potential of a domain $\Omega \supset \partial D$, with a prescribed volume on $\Omega \setminus D$. Our main goal is to establish uniqueness and symmetry results when $\partial D$ has a given geometric property. Full regularity of the free boundary is obtained under these symmetry conditions imposed on the fixed boundary.

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Teixeira Eduardo: Uniqueness, symmetry and full regularity of free boundary in optimization problems with volume constraint. Interfaces Free Bound. 9 (2007), 133-148. doi: 10.4171/IFB/159