Math 265B Lecture 1

Fall 2008

Real Analysis for Applications

Instructor: Luminita VESE
Lecture Meeting Time: MWF 12:00P-12:50P
Lecture Location: MS 7608
Office Hours: MWF 2-3pm or by appointment, at MS 7620-D.

Topics: (tentative) Abstract variational principles, L^p, Sobolev and BV spaces, representation of functionals, general measure and integrations, Fubini and Radon-Nikodym theorems, Fourier integrals, applications to partial differential equations and variational problems

Suggested References: (most of them placed on reserve at SEL library)

  • G.B. Folland, Real analysis: modern techniques and their applications, John Wiley & Sons, 1999 (2nd edition)
  • L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press 1992.
  • L.C. Evans, Partial Differential Equations , AMS 1998.
  • R.A. Adams, Sobolev Spaces , Academic Press 1975.
  • H. Attouch, G. Buttazzo, and G. Michaille, Variational Analysis in Sobolev and BV Spaces: applications to PDE's and optimization, MPS-SIAM 2006.
  • L. Ambrosio, N. Fusco, D. Pallara, Functions of bounded variation and free discontinuity problems , Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 2000.

    Grading: will be based on participation and homeworks.

    Homeworks: will be assigned (weekly or bi-weekly) and posted on the class webpage.

    HW #1

    HW #2

    HW #3

    HW #4

    HW #5

    HW #6
    HW6.tex

    Notes