Abstracts
- Maximum principles and their applications (C. Enache): In this course we will discuss about the maximum principles and their applications to the study of partial differential equations. More precisely, we will show how one may employ such maximum principles in problems of physical or geometrical interest, in order to get a priori estimates, isoperimetric inequalities, symmetry results, convexity results, the shape of some free boundaries, Liouville type results and some decay estimates.
- Nonlinear partial differential equations arising in differential geometry in the study of minimal or constant mean curvature surfaces (M. Lucia): With the development of the calculus many mathematicians have applied this powerful tool to study of geometric properties of curves and surfaces. Geometrical objects like minimal surfaces or CMC (constant mean curvature) surfaces have led to study interesting nonlinear partial differential equations that are still object of investigations. The aim of this lecture will be to introduce the underlying background to understand some of these geometrical problems, and how they can be solved using PDE techniques or tools arising from the calculus of variations.