Calculus of Variations and Geometric Measure Theory

J. J. Alibert - G. Bouchitté - I. Fragalà - I. Lucardesi

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

created by lucardesi on 10 Aug 2018


Published Paper

Inserted: 10 aug 2018
Last Updated: 10 aug 2018

Journal: Interfaces and Free Boundaries
Volume: 15
Number: 1
Pages: 95-119
Year: 2013
Doi: 10.4171/IFB/296
Links: IFB web site


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.