The goal of this course is to give an introduction to the theory of distributions and cover the fundamental results of Sobolev spaces including fractional spaces that appear in the interpolation theory. Those notions are central to the study of partial dif ...
Introduction to classical Calculus of Variations and a selection of modern techniques. The Calculus of Variations aims at showing the existence of minimisers (or critical points) of functionals that naturally appear in mathematics and physics (Dirichlet en ...
The first part is devoted to Monge and Kantorovitch problems, discussing the existence and the properties of the optimal plan. The second part introduces the Wasserstein distance on measures and develops applications of optimal transport to PDEs, functiona ...
The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions. ...
This is an introductory course on Elliptic Partial Differential Equations. The course will cover the theory of both classical and generalized (weak) solutions of elliptic PDEs. ...
The goal of this course is to present an overview on the solvability and the regularity of relevant models of physical, technological and economical systems, which may be formulated as minimization problems of suitable integral functionals. ...