Schema della sezione

  • The main topic of the course is  Advanced Functional Analysis. 

    Schedule: Monday, Wednesday and Thursday 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., 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

    Sheets of exercises will be given during the course. Solving problems and exercise is very useful for the study and the preparation of the exam.  Two Problems Sessions  will be organized during the course (one in November, one in December)

     

    The class of Thursday 19 November is shortened , with new timetable 14.30-15.30 due to the decision of the CCS President to allow participation in the  UMI meeting