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

Abstract : 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.
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https://hal-univ-tln.archives-ouvertes.fr/hal-00993897
Contributor : Jean-Jacques Alibert <>
Submitted on : Tuesday, May 20, 2014 - 5:08:38 PM
Last modification on : Tuesday, August 13, 2019 - 11:10:04 AM

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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 Boundaries, 2013, 15 (1), pp.95-119. ⟨10.4171/IFB/296⟩. ⟨hal-00993897⟩

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