Orateur
Ilias Ftouhi
Description
In this talk, we address the problem of maximizing the supremum norm of the gradient of the torsion function over planar convex domains with fixed measure (or perimeter). We prove that an optimal shape exists, its boundary possesses $C^1$ regularity, and it features at least one straight segment. The proofs leverage probabilistic methods along with a novel boundary Harnack principle for the torsion function. The talk is based on a joint work with Krzysztof Burdzy (University of Washington) and Phanuel Mariano (Union College).