Geodesic
An overdetermined problem with non-constant boundary condition
Chiara Bianchini1 ; Antoine Henrot2 ; Paolo Salani1
1Università degli Studi di Firenze, Italy
2Université de Lorraine, Vandoeuvre-les-Nancy, France
Interfaces and free boundaries, Tome 16 (2014) no. 2, pp. 215-241

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DOI

We investigate an overdetermined torsion problem, with a non-constant positively homogeneous boundary constraint on the gradient. We interpret this problem as the Euler equation of a shape optimization problem, we prove existence and regularity of a solution. Moreover several geometric properties of the solution are shown.
DOI : 10.4171/ifb/318
Classification : 35-XX, 49-XX
Mots-clés : Torsion problem, overdetermined problem, shape optimization

Chiara Bianchini  1   ; Antoine Henrot  2   ; Paolo Salani  1

1 Università degli Studi di Firenze, Italy
2 Université de Lorraine, Vandoeuvre-les-Nancy, France 
Chiara Bianchini; Antoine Henrot; Paolo Salani. An overdetermined problem with non-constant boundary condition. Interfaces and free boundaries, Tome 16 (2014) no. 2, pp. 215-241. doi: 10.4171/ifb/318
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     doi = {10.4171/ifb/318},
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