401-3350-21L Classical Theory of Elliptic Partial Differential Equations
| Semester | Spring Semester 2021 |
| Lecturers | J. Serra |
| Periodicity | non-recurring course |
| Language of instruction | English |
| Comment | Number of participants limited to 12. |
Courses
| Number | Title | Hours | Lecturers | ||||
|---|---|---|---|---|---|---|---|
| 401-3350-21 S | Classical Theory of Elliptic Partial Differential Equations | 2 hrs |
| J. Serra |
Catalogue data
| Abstract | Following the book "Elliptic Partial Differential Equations" of Qing Han and Fanhua Lin, the seminar will cover ---from an introductory perspective--- some important classical tools and results in the standard theory of Elliptic PDE |
| Learning objective | To present some of the most useful classical tools and results in nonlinear Elliptic PDE (weak and viscosity solutions and their maximum principles, moving plane method, Bernstein's technique, De Giorgi-Nash-Moser Harnack Inequality, etc.) |
| Content | (flexible depending on the background of the students) -Review of harmonic functions -Weak and viscosity solutions -Maximum principles and barriers -Moving plane method -Bernstein's technique -Schauder estimates (review) -De Giorgi-Nash-Moser and Hölder continuity of gradients |
| Literature | Elliptic Partial Differential Equations: Second Edition Qing Han and Fanghua Lin Publication Year: 2011 ISBN-10: 0-8218-5313-9 ISBN-13: 978-0-8218-5313-9 Courant Lecture Notes, vol. 1.R |
| Prerequisites / Notice | Although many parts of the book are rather self-contained, it would be advisable to have followed before the bachelor course Functional Analysis II |
Performance assessment
| Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
| ECTS credits | 4 credits |
| Examiners | J. Serra |
| Type | ungraded semester performance |
| Language of examination | English |
| Repetition | Repetition only possible after re-enrolling for the course unit. |
Learning materials
| No public learning materials available. | |
| Only public learning materials are listed. |
Groups
| No information on groups available. |
Restrictions
| Places | Limited number of places. Special selection procedure. |
| Beginning of registration period | Registration possible from 04.01.2021 |
| Priority | Registration for the course unit is only possible for the primary target group |
| Primary target group | Mathematics BSc (404000)
starting semester 06 Mathematics MSc (437000) Applied Mathematics MSc (437100) |
| Waiting list | until 01.03.2021 |
| End of registration period | Registration only possible until 19.02.2021 |
Offered in
| Programme | Section | Type | |
|---|---|---|---|
| Mathematics Bachelor | Seminars | W |  |
| Mathematics Master | Seminars | W | |