SF2723 Selected topics in Mathematics:

Partial Differential Equations

Fall term 2014

Questions And Instructions For The Oral Exam

Teacher: John Andersson

First Meeting: September 2nd from 13-15 in Room 3733. Subsequently we will meet most Tuesdays from 13-15 in 3733. However, due to clashes in my schedule some weeks we will meet at another time.

Course plan.

Course Literature: The course literature will be published here in installments:

Chapters 1 (This link contains the material we will cover in the first two lectures. Version 4 Sept)

Chapters 2 (Material for the third lecture and maybe the fourth lecture, version 21st September, some changes from the previous version)

Chapters 3 (Material for the forth 5th and beginning of 6th lecture, version 15th September)

Chapters 4 (Material for the 6th and seventh lecture, version 13th October.)

Chapters 5 (Material for the 8th and 9th lecture, version 6th November – some typos fixed.)

Chapters 6 (Material for the November 11 and November 18 and maybe November 25, version 25th November)

Chapters 7 (Material for the 2nd December, version 30th November)

All the course notes - or 179 pages of typos. (This link contains all the theory of the course. Somehow I will try to proofread it over the weekend and add an updated version as soon as I can. Last changed December 16th.)

Course content: We will discuss several aspects of the theory of elliptic PDE. In particular we will cover potential theoretic aspects, Perron's method, some functional analytic methods. Different kinds of solutions (classical, weak and viscosity).

The basic goal of the course is to give the participant an orientation of PDE theory and the idea of some of the commonly used techniques. As a meta-narrative we will try to convince the participants of the need for an abstract theory of PDE with much stress on apriori estimates.

Homework assignments. The first homework can be downloaded here: Homework 1. A complete solution should be handed in on the 21st of October.

The second homework assignment can be downloaded here: Homework 2. A complete solution should be handed in before the 19th December, preferably during the lecture on the 16th.

Examination:

There will be TWO homework assignments that will appear on this web page.

At the end of the course there will be an oral exam.

Lectures: The following notes are just my one notes scanned. They are not intended as study material (and are even more devoid of pedagogical thinking than my lectures). However, they might serve as a, not so gentle, reminder of the material covered during the lecture.

Lecture 1

Lecture 2

Lecture 4

Lecture 5

Lecture 6

Lecture 7

Lecture 8

Lecture 9 (The Pdf file states that it is lecture 8 – but it is really lecture 9.)

Lecture 10

Lecture 11

Lecture 12

Lecture 13