JournalsifbVol. 15, No. 1pp. 95–119

A nonstandard free boundary problem arising in the shape optimization of thin torsion rods

  • Jean Jacques Alibert

    Université de Toulon et du Var, La Garde, France
  • Guy Bouchitté

    Université de Toulon et du Var, La Garde, France
  • Ilaria Fragalà

    Politecnico di Milano, Italy
  • Ilaria Lucardesi

    Politecnico di Milano, Italy
A nonstandard free boundary problem arising in the shape optimization of thin torsion rods cover
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Abstract

We study a 2dd-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 DD. 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 DD, and we study the nonstandard free boundary problem with a gradient obstacle, which is obtained through the optimality conditions.

Cite this article

Jean Jacques Alibert, Guy Bouchitté, Ilaria Fragalà, Ilaria Lucardesi, A nonstandard free boundary problem arising in the shape optimization of thin torsion rods. Interfaces Free Bound. 15 (2013), no. 1, pp. 95–119

DOI 10.4171/IFB/296