# Functional Analysis

## PDE and Functional Analysis

Winter Term 2014/2015

### Lectures

Wednesday 10–12 and Friday 8–10 in the small lecture hall (KHS We10)

### Classes

There are three tutorial groups:

- Monday 12–14, room N0.003, tutor R. Höfer
- Wednesday 16–18, room 218 (2.030) AVZ I, tutor S. Wolfers
- Thursday 12–14, room N0.007, tutor I. Zachhuber

### Problem Sheets

Problem sheets are handed out every Friday in the lecture. Solutions are collected also during the lecture on Fridays. They may be submitted in groups of two students who attend the same tutorial.

### Examination

The course is completed by a written examination:

- 1st exam: Monday, 23.02.2015, 9–12, GHS (Wegelerstr. 10)
- 2nd exam: Saturday, 14.03.2015, 9–12, GHS (Wegelerstr. 10)

Arrive to the exam in time and have your student id and a photo id ready for inspection. The exam is closed book, that is, no aids are permitted.

The examination results will be availbale a few days after the exam. You are welcome to review your graded second exam

- Wednesday, 18.03.2015 from 2.15 to 3.00 pm in room 2.040 (Endenicher Allee 60).

For general information on examinations see here for Bachelor and Master studies.

### Synopsis

The course covers basic functional analytic methods and their application to partial differential equations such as

- Banach spaces, Hahn-Banach Theorem, Banach-Steinhaus Theorem, weak convergence
- Lebesgue- and Sobolev-spaces
- Hilbert spaces, Lax-Milgram Theorem, spectral theory
- elliptic PDEs

### Literature

There are many books on functional analysis, for instance

- H. W. Alt.
*Lineare Functionalanalysis*. Springer. - H. Brezis.
*Functional Analysis and Partial Differential Equations*. Springer. - M. Reed und B. Simon.
*Methods of modern mathematical physics. Volume 1: Functional Analysis*. Academic Press.