# Functional Analysis

## Nonlinear PDEs I

Winter 2015/2016

### Lectures

Mondays and Thursdays 10–12, SR 1.008

Prof. Dr. J. J. L. Velázquez

### Classes

Tuesday 14–16, room N0.003

Wednesday 14–16, room SR 0.011

### Examination

The course is completed by an exam on 15./16.02.2016 and 15./16.03.2016. Slots for the first date will be allocated in due course.

In order to sit the exam students have to get at least 50% of the overall marks of the problem sheets as requirement for passing the classes.

### Synopsis and Prerequisites

The course covers basic theory (existence, uniqueness, regularity) for weak solutions of nonlinear elliptic and parabolic PDEs.

A sound knowledge of linear PDEs and functional analysis is essential.

### Problem sheets

Problem sheets are handed out in the lecture on Thursdays and are available below. Solutions may be submitted in groups of two students who attend the same tutorial and are collected on Thursdays during the lecture.

Problem Sheet 01 (16 points, due 29.10.15)

Problem Sheet 02 (16 points, due 05.11.15)

Problem Sheet 03 (16 points, due 12.11.15)

Problem Sheet 04 (16 points, due 19.11.15)

Problem Sheet 05 (16 points, due 26.11.15)

Problem Sheet 06 (16 points + 4 extra points, due 03.12.15)

Problem Sheet 07 (16 points, due 10.12.15)

Problem Sheet 08 (16 points, due 17.12.15)

Problem Sheet 09 (12 points + 8 extra points, due 07.01.16)

Problem Sheet 10 (12 points + 4 extra points, due 14.01.16)

Problem Sheet 11 (16 points, due 21.01.16)

Problem Sheet 12 (due 28.01.16 if you want it marked)

Problem Sheet 13 (due 04.02.16 if you want it marked)

Total: 168 points, 16 extra points

### Literature

- L. C. Evans. Partial Differential Equations. Graduate Studies in Mathematics vol. 19, American Mathematical Society, 1991.
- M. Giaquinta. An introduction to regularity theory for nonlinear elliptic systems. Lectures in Mathematics ETH Zürich, Birkhäuser, 1993.
- D. Gilbarg, N. Trudinger. Elliptic Partial Differential Equations of Second Order. Springer-Verlag, 1977.
- G. Stampacchia. Équations elliptiques du second ordre à coefficients discontinus. Presse de l'Universite Montreal, 1966.