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. |
| 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 |