Geodesic
A nonstandard free boundary problem arising in the shape optimization of thin torsion rods
Jean Jacques Alibert1 ; Guy Bouchitté1 ; Ilaria Fragalà2 ; Ilaria Lucardesi2
1Université de Toulon et du Var, La Garde, France
2Politecnico di Milano, Italy
Interfaces and free boundaries, Tome 15 (2013) no. 1, pp. 95-119

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DOI

We study a 2d-variational problem, in which the cost functional is an integral depending on the gradient through a convex but not strictly convex integrand, and the admissible functions have zero gradient on the complement of a given domain D. We are interested in establishing whether solutions exist whose gradient “avoids” the region of non-strict convexity. Actually, the answer to this question is related to establishing whether homogenization phenomena occur in optimal thin torsion rods. We provide some existence results for different geometries of D, and we study the nonstandard free boundary problem with a gradient obstacle, which is obtained through the optimality conditions.
DOI : 10.4171/ifb/296
Classification : 49-XX, 35-XX, 00-XX
Mots-clés : Convexity, free boundary problems, Cheeger sets, thin torsion rods

Jean Jacques Alibert  1   ; Guy Bouchitté  1   ; Ilaria Fragalà  2   ; Ilaria Lucardesi  2

1 Université de Toulon et du Var, La Garde, France
2 Politecnico di Milano, Italy 
Jean Jacques Alibert; Guy Bouchitté; Ilaria Fragalà; Ilaria Lucardesi. A nonstandard free boundary problem arising in the shape optimization of thin torsion rods. Interfaces and free boundaries, Tome 15 (2013) no. 1, pp. 95-119. doi: 10.4171/ifb/296
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     title = {A nonstandard free boundary problem arising in the shape optimization of thin torsion rods},
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     pages = {95--119},
     year = {2013},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/296/}
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