# Math 265B Lecture 1

## Winter 2014

## Real Analysis for Applications

Instructor:
Luminita VESE

Lecture Meeting Time: Monday and Wednesday 4pm-5.20pm.

Lecture Location: BH 5422

Office Hours: TBA or by appointment.

** 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:**

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

Latex file

HW #2

Latex file

Notes