2018/2019

2018/2019

DM270

MAT/05 (MATHEMATICAL ANALYSIS)

DEPARTMENT OF MATHEMATICS "FELICE CASORATI"

MATHEMATICS

PERCORSO COMUNE

1°

2nd semester (04/03/2019 - 14/06/2019)

6

48 lesson hours

Italian

ORAL TEST

SEGATTI ANTONIO GIOVANNI (titolare) - 3 ECTS
SANTAMBROGIO FILIPPO AMBROGIO - 3 ECTS

Basic knowledges of functional analysis and geometric measure theory.

The goual of the course is to give an introduction to Calculus of Variations

Program:
1) One dimensional calculus of variations with examples and applications to geodesics, brachistocrone, mechanical models. Euler Equations
2)Lower semicontinuity and convexity
3) Convex duality and application to regularity
4)Harmonic and quasi-harmonic functions. Campanato spaces and Holderian regularity
5)Infinity laplacian
6)Isoperimetric problem
7) Gamma-convergence: definitions and significative examples
4)

G. Buttazzo, M. Giaquinta, S. Hildebrandt: “One-dimensional Variational Problems, an Introduction”.
Oxford University Press, 1998
E. Giusti: “Direct Methods in the Calculus of Variations”. World Scientific 2003.
A. Braides: “Gamma-convergence for beginners”. Oxford University Press, 2002

Oral examination