L-Infinity Variational Problems on Graphs: Applications and Continuum Limits

Thursday, September 17, 2020 - 9:30am - 10:15am
Leon Bungert (Friedrich-Alexander-Universität Erlangen-Nürnberg), Tim Roith (Friedrich-Alexander-Universität Erlangen-Nürnberg)
The talk is divided into two parts. In the first part we review L-infinity type variational problems on graphs which are motivated by applications in (semi-supervised) machine learning. In particular, we study ground states of the sup-norm of the gradient, characterize them as distance functions and relate them to the asymptotic behavior of the associated gradient flow. In the second part we study continuum limits using the tools of Gamma-convergence and apply the results to the Lipschitz extension problem, ground states and gradient flows.