Calculus of Variations and Geometric Measure Theory

Variational methods and applications

Some new results on the prescribed mean curvature problem

Gian Paolo Leonardi (Department of Mathematics, University of Trento)

created by paolini on 08 Sep 2021
modified on 14 May 2022

9 sep 2021 -- 10:20   [open in google calendar]


Finding graphs of prescribed mean curvature is one of the classical problems of Calculus of Variations. This problem is closely connected with non-parametric minimal surfaces, and it is strongly motivated by capillarity theory. After an introduction of the classical formulation together with some milestone results, we will describe some recent progress obtained in two different directions. First, the relaxation of the regularity assumptions on the domain, leading to the "weak-regularity" hypothesis. Second, the prescribed mean curvature measure problem.