Mathematics | University of Parma

Professor
Academic discipline: Analisi matematica (MAT/05)
Field: Attività formative affini o integrative
Type of training activity: Related/supplementary

48 hours
of face-to-face activities

6 credits

hub: PARMA

course unit
in - - -

lectures timetable unavailable

exam calls

Learning objectives

The course aims at providing a first introductory and yet significant knowledge on
the problems and the methods of the Calculus of Variations.

Prerequisites

Basic knowledge of Analysis and Measure Theory, and Sobolev Spaces

Course unit content

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 Ndimensions,
we will expose De Giorgi's regularity theory.

Full programme

- - -

Bibliography

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.

Teaching methods

The course will consist in lectures delivered at the blackboard. The topics will be
complemented with motivations, instructive exercises and applications. Emphasis
will be placed on the mathematical rigor of the presentation, which will be as much
detailed and self-contained as possible.

Assessment methods and criteria

The final exam will consist in an oral interview, aiming at evaluating the learning
ability of the student and the quality and rigor of his/her exposition.

Other information