Section outline

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

    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., 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

    The exam will be structured as follows:  1 hour (or less) to answer (in writing) to 2/3 questions (see the list of questions from the past exams), followed by a short colloquium with the teacher. 

    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. 

    Dates of the exams:

    Monday December 22, from 11, room 2AB40

    Tuesday December 23, from 10, room 1BC45

    Friday January 9,  from 14.30, room 1BC50

    Monday January 19, from 14 (in the afternoon), room 2AB40

    Tuesday February 17, from 10 (in the morning), room  2AB40

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