Researcher: Yury Korolev, and Carola-Bibiane Schönlieb

We study minimisers of Rayleigh quotients involving $L^\infty$ type norms such as the $W^{1,\infty}$ Sobolev norm. Notable minimisers include ground states of the $\infty$-Laplacian $\Delta_\infty$, $\infty$-harmonic functions and the distance function.  We use convex analysis to characterise these minimisers and their subgradients.