28407 - Calculus of Variations 1

Course Unit Page

  • Teacher Bruno Franchi

  • Credits 6

  • SSD MAT/05

  • Language Italian

  • Campus of Bologna

  • Degree Programme First cycle degree programme (L) in Mathematics (cod. 8010)

Academic Year 2019/2020

Learning outcomes

At the end of the course, the student knows the basic notion of the calculus of variations. He can apply the acquired knowledge to understanding and solving model problems of electrostatics, mechanics and science of materials.

Course contents

Regularity of the solutions of Dirichlet problem for linear elliptic equations. Applications to approximation schemes. Minima of convex functionals and their regularity. Sobolev and Poincaré inequalities. Rellich theorems. Introduction to homogenization theory.


H. Brezis, Sobolev Spaces and Partial Differential Equations, Springer, New York.

Further references will be provided during the course.

Teaching methods

Lectures at the blackboard.

Assessment methods

The final exam aims to verify the achievement of the following educational objective: - coherent presentation of some topics of the course, giving evidence of having fully understood the fundamental concepts and the deduction mechanisms. The exam will consist of an oral interview or a short seminar on topics close to those of the course and that use tools and methods.

Office hours

See the website of Bruno Franchi