# Leon Bungert: Tackling L∞ eigenvalue problems with convex analysis

**Time: **
Thu 2022-09-22 15.00 - 16.00

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

**Video link: **
Meeting ID: 921 756 1880

**Participating: **
Leon Bungert (University of Bonn)

**Abstract:**

I will characterize the L∞ eigenvalue problem which is solved by stationary points of the Rayleigh quotient \(∥∇u∥_{L^{\infty}}/∥u∥_∞ \)and relate it to a divergence-form PDE, similarly to what is known for \(L^p\) eigenvalue problems and the p-Laplacian for p < ∞. Contrary to most existing methods, which study \(L^{\infty}\)-problems as limits of \(L^p\)-problems for large values of p, I shall present a novel framework for analyzing the limiting problem directly using convex analysis and measure theory. Our results rely on a novel fine characterization of the subdifferential of the Lipschitz-constant-functional. I also study a dual Rayleigh quotient whose minimizers solve an optimal transport problem associated to a generalized Kantorovich--Rubinstein norm. This is joint work with Yury Korolev and based on the article (https://arxiv.org/abs/2107.12117).