Orateur
Ilias FTOUHI
Description
We consider the shape optimization problem of looking for the shape that maximizes the maximal norm of the gradient of the torsion function among planar convex sets with a prescribed measure (or perimeter). We prove the existence of such a shape and prove that its boundary is C^1 regular. Then, we show that its boundary contains a segment. The proofs are mainly based on probabilistic arguments and a novel version of the boundary Harnack principle for the torsion function. This is a work in collaboration with Krzysztof Burdzy (University of Washington) and Phanuel Mariano (Union College).