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Do optimal thin torsion rods contain homogenized regions ?

In this seminar I will present a problem arising in the optimal design of thin torsion rods. Establishing whether homogenization phenomena occur or not turns out to be equivalent to a non standard free boundary problem with gradient obstacle in 2d, set on the section of the rod. I will present some existence results and qualitative properties, although the complete answer to the problem is still open.

CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46