Talk by Julio D. Rossi
On June 30th, 2021, Prof. Dr. Julio D. Rossi (Universidad de Buenos Aires) gave a talk about "Convexity and its associated equation" as part of the research seminar Analysis of the FernUniversität in Hagen.
Our goal in this talk is to look at the notion of convexity and the equations associated with the convex envelope of a partial datum in different contexts.
In the first part of this talk we describe with PDEs given in terms of eigenvalues of the Hessian and their relation with classical concave/convex functions. Next, we will introduce a fractional version of the involved ideas.
In the second part we will describe a notion of convexity for functions defined on a regular tree and on a compact metric graph.
Based on joint works with P. Blanc, N. Frevenza, L. Del Pezzo and Alexander Quaas.