Joaquim Serra: Catalogue data in Spring Semester 2021 |
| Name | Prof. Dr. Joaquim Serra |
| Field | Mathematics |
| Address | Professur für Mathematik ETH Zürich, HG J 54 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telephone | +41 44 632 50 60 |
| joaquim.serra@math.ethz.ch | |
| Department | Mathematics |
| Relationship | Associate Professor |
| Number | Title | ECTS | Hours | Lecturers | |
|---|---|---|---|---|---|
| 401-3350-21L | Classical Theory of Elliptic Partial Differential Equations  Number of participants limited to 12. | 4 credits | 2S | J. Serra | |
| 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 | ||||
| 401-5350-00L | Analysis Seminar  | 0 credits | 1K | A. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, M. Iacobelli, L. Kobel-Keller, T. Rivière, J. Serra, University lecturers | |
| Abstract | Research colloquium | ||||
| Learning objective | |||||
| Content | Research seminar in Analysis | ||||