Calculus of Variations and Geometric Measure Theory

Geometric and analytic aspects of $\infty$-Poincar\'e inequalities

Nageswari Shanmugalingam (University of Cincinnati)

created by ambrosio on 02 May 2018

14 may 2018 -- 10:00   [open in google calendar]

Scuola Normale Superiore, Aula Marie Curie


The study of absolute minimizing Lipschitz extensions and infinity-harmonic functions in the Euclidean setting was initiated by Aronsson, Crandall and Evans, and is of great interest now, with optimal regularity of solutions yet open. In the metric setting, and indeed even in the weighted Euclidean setting, studies of such solutions are possible under certain conditions on the metric space. One condition is the existence of $\infty$-harmonic function. In this talk we will discuss this inequality, and a geometric and analytic characterizations of this inequality.