Schema della sezione

  • Schedule: Monday, Tuesday and Wednesday, 14.30-16.10, room 1BC50
    Plan of the course

    • Part 0: Preliminaries  (calculus and measure theory) [F, chapter 1], [E, appendices]
    • Part 1: Elements of Geometric Measure Theory. Radon measures and Riesz theorem. Hausdorff measures.  [EG, chapters 1,2] [F, chapter 7]
    • Part 2: The theory of distributions [F, chapter 9]
    • Part 3: Sobolev spaces [E chapter 5]
    • Part 4: Functions of  bounded variation [EG, chapter 5]

    Main references

    • [EG] Evans L.C.,and   Gariepy,  F.C., Measure theory and fine properties of functions, Boca Raton, CRC Press, 1992.
    • [E] Evans, L.C., Partial Differential Equations, American Mathematical Soc., 2010. 
    • [F] Folland, G.B., Real Analysis. New York: Wiley Interscience, 1999.

    Other references: 

    • Ambrosio, L.Corso introduttivo alla teoria geometrica della misura e alle superfici minime, Pisa, Scuola Normale Superiore, 2009.
    • Ambrosio, L., Fusco, N., and Pallara, D., Functions of bounded variations and free discontinuity problems, Oxford Mathematical Monographs, 2000.
    • Brezis, H.,Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer 2011

    Dates of the exams:

    Monday December 22, from 11, room 2AB40

    Friday January 9,  from 14.30, room 1BC50

    Monday January 20, from 14 (in the afternoon), room 1BC50 

    Friday February 14, from 10 (in the morning), room 1BC50.

    It is possible to take the exam also in other dates (also in December!), by prior agreement with me.