This course differs from the approach taken in Math 362 which focuses on solutions in classical function spaces via Greens functions. It may therefore be taken by students who have attended Math 362, but we will again start from basic principles so that Math 362 is not a prerequisite.
| Instructor: | Marcel Oliver |
| Email: | m.oliver@jacobs-university.de |
| Phone: | 200-3212 |
| Office hours: | Tu, Th 11:15 in Research I, 107 |
| Grader: | Mahmut Çalik |
| Email: | m.calik@jacobs-university.de |
| Lectures: | Tu 9:45 and Th 8:15 in East Hall 8 |
| Homework: | 30% |
| Midterm Exam: | 30% |
| Final Exam: | 40% |
| 03/09/2009: | Introduction; weak derivatives |
| 08/09/2009: | Sobolev spaces Wk,p; properties of weak derivatives |
| 10/09/2009: | Convolution, mollifiers, and approximation by smooth functions |
| 15/09/2009: | Extensions |
| 17/09/2009: | Traces |
| 22/09/2009: | Sobolev inequalities |
| 24/09/2009: | Compact embeddings |
| 29/09/2009: | Second order elliptic equations: definitions and weak solutions |
| 01/10/2009: | Lax-Milgram theorem, energy estimates |
| 06/10/2009: | Fredholm alternative, existence theorems for weak solutions |
| 08/10/2009: | Interior regularity |
| 13/10/2009: | No class, Reading Day |
| 15/10/2009: | Regularity up to the boundary |
| 20/10/2009: | Maximum principles |
| 22/10/2009: | Midterm review |
| 27/10/2009: | Midterm Exam |
| 29/10/2009: | Parabolic equations (5 classes) |
| 03/11/2009: | |
| 05/11/2009: | |
| 10/11/2009: | |
| 12/11/2009: | |
| 17/11/2009: | Selected nonlinear problems (5 classes) |
| 19/11/2009: | |
| 24/11/2009: | |
| 26/11/2009: | |
| 01/12/2009: | |
| 03/12/2009: | Review for final exam |
| 15/12/2009: | Final Exam, 16:00-18:00 in East Hall 4 |