- Docente: Eleonora Cinti
- Crediti formativi: 6
- SSD: MAT/05
- Lingua di insegnamento: Italiano
- Moduli: Eleonora Cinti (Modulo 1) Berardo Ruffini (Modulo 2)
- Modalità didattica: Convenzionale - Lezioni in presenza (Modulo 1) Convenzionale - Lezioni in presenza (Modulo 2)
- Campus: Bologna
- Corso: Laurea Magistrale in Matematica (cod. 5827)
Conoscenze e abilità da conseguire
At the end of the course, the student has a knowledge of some advanced chapters of classical and direct methods in calculus variations, with application to some topic of deep recent interest.
Contenuti
Direct method of Calculus of Variations.
Existence of minimizers in the class of Lipschitz functions.
The area functional.
BV functions and their main properties.
Sets of finite perimeter and their main properties.
Existence of minimizers for geometric problems in the class of sets of finite perimeter.
Reduced boundary and De Giorgi's structure Theorem.
The isoperimetric problem and related topics.
Rearrangement inequalities. The Pòlya-Szego inequality, the Hardy-Riesz-Sobolev inequality and some applications.
An introduction to Gamma-convergence, the Modica-Mortola Theorem.
Testi/Bibliografia
Luigi Ambrosio, Nicola Fusco, Diego Pallara, "Functions of Bounded Variations and Free Discontinuity Problems.
L.C. Evans, L. F Gariepy, "Measure Theory and Fine Properties of Functions".
Enrico Giusti, "Direct Methods in the Calculus of Variations".
Enrico Giusti, "Minimal Surfaces and Functions of Bounded Variations".
Francesco Maggi, "Sets of Finite Perimeter and Geometric Variationsl Problems.
Metodi didattici
Frontal lectures
Modalità di verifica e valutazione dell'apprendimento
Oral exam
Strumenti a supporto della didattica
The suggested Textbooks.
Orario di ricevimento
Consulta il sito web di Eleonora Cinti
Consulta il sito web di Berardo Ruffini