Geodesic
Uniqueness, symmetry and full regularity of free boundary in optimization problems with volume constraint
Eduardo V. Teixeira1 orcid
1Universidade Federal do Ceará, Fortaleza, Brazil
Interfaces and free boundaries, Tome 9 (2007) no. 1, pp. 133-148

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DOI

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 ∫∂D​Γ(uμ​)dσ, where D is a fixed domain and u is the potential of a domain Ω⊃∂D, with a prescribed volume on Ω∖D. Our main goal is to establish uniqueness and symmetry results when ∂D has a given geometric property. Full regularity of the free boundary is obtained under these symmetry conditions imposed on the fixed boundary.
DOI : 10.4171/ifb/159
Classification : 35-XX, 65-XX, 76-XX, 92-XX

Eduardo V. Teixeira  1

1 Universidade Federal do Ceará, Fortaleza, Brazil 
Eduardo V. Teixeira. Uniqueness, symmetry and full regularity of free boundary in optimization problems with volume constraint. Interfaces and free boundaries, Tome 9 (2007) no. 1, pp. 133-148. doi: 10.4171/ifb/159
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     title = {Uniqueness, symmetry and full regularity of free boundary in optimization problems with volume constraint},
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     pages = {133--148},
     year = {2007},
     volume = {9},
     number = {1},
     doi = {10.4171/ifb/159},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/159/}
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