- Docente: Bruno Franchi
- Credits: 6
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
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from Feb 20, 2024 to May 29, 2024
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
Complements of Functional Analysis. Regularity of the solutions of Dirichlet problem for linear and nonlinear elliptic equations. Applications to approximation schemes. Minima of convex functionals and their regularity. Sobolev and Poincaré inequalities. Rellich theorems. BV spaces, perimeter and isoperimetric inequalities. Introduction to homogenization theory.
Readings/Bibliography
H. Brezis, Sobolev Spaces and Partial Differential Equations, Springer, New York.
L. Evans & R.F. Gariepy, Ronald F., Measure theory and fine properties of functions. Revised edition. CRC Press, Boca Raton, FL,2015.
Further readings 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.
Assessment criteria and assessment thresholds:
30 cum laude: Excellent, excellent solidity of knowledge, excellent expressive properties and excellent understanding of the concepts.
30: Very good, complete and adequate knowledge, well-articulated and correctly expressed.
27-29: Good, satisfactory knowledge, essentially correct expression.
24-26: Fairly good knowledge, but not complete and not always correct.
21-23: Generally sufficient knowledge but superficial. Expression is often not appropriate and confused.
18-21: Sufficient. The expression and articulation of the speech show important gaps.
Office hours
See the website of Bruno Franchi