ADVANCED ANALYSIS 2
Learning outcomes of the course unit
The course aims at providing a first introductory and yet significant knowledge on the problems and the methods of the Calculus of Variations. It will set up the fundamental tools needed to access and understand the topics of contemporary research.
Basic knowledge of Analysis and Measure Theory
Course contents summary
The course is focused on some classical topics of the Calculus of Variations. It is divided in two parts. The first one deals with a thorough study of firts and second order necessary and sufficient minimality conditions for one-dimensional problems. Among the various examples, a complete treatment of the brachistochrone problem will be given. The second part is devoted to the DIrect Methods of the Calculus of Variations: after proving a general existence theorem for integral functionals in N-dimensions, we will expose De Giorgi's regularity theory.
No specific reference textbooks. The topics of the course are chosen by the instructor and may be found in several different classical books on the Calculus of Variations.
Assessment methods and criteria