Abstract: In this minicourse we will describe the convex envelope of a given boundary datum in terms of being a solution to a partial differential equation (PDE). The ambient space will be a smooth convex domain in the Euclidean space and we will consider different notions of convexity.

Since the partial differential equations that arise are not in divergence form, we will first briefly describe the theory of viscosity solutions. Next, we will describe different notions of convexity and introduce the convex envelope of a boundary datum. Our main goal is then to obtain a PDE that characterizes this convex envelope. Finally, if time allows, we will also describe a connection with game theory.

This minicourse will combine ideas from PDEs and probability theory and will try to be self contained.

Schedule and location

Lecture 1 (ICMAT, Aula Gris 2): November 6th, 10:30 - 12:30. 

Lecture 2 (UAM, Módulo 17, 520): November 7th, 10:30 - 12:30. 

Lecture 3 (ICMAT, Aula Gris 2): November 7th, 15:00 - 17:00. 

Lecture 4 (UAM, Modulo 17, 520): November 8th, 10:30 - 12:30. 

No registration is needed and everybody is welcome to attend