Joaquim Serra: Catalogue data in Spring Semester 2021

Name Prof. Dr. Joaquim Serra
Professur für Mathematik
ETH Zürich, HG J 54
Rämistrasse 101
8092 Zürich
Telephone+41 44 632 50 60
RelationshipAssociate Professor

401-3350-21LClassical Theory of Elliptic Partial Differential Equations Restricted registration - show details
Number of participants limited to 12.
4 credits2SJ. Serra
AbstractFollowing 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
ObjectiveTo 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
LiteratureElliptic 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 / NoticeAlthough many parts of the book are rather self-contained, it would be advisable to have followed before the bachelor course Functional Analysis II
401-5350-00LAnalysis Seminar Information 0 credits1KA. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, M. Iacobelli, L. Kobel-Keller, T. Rivière, J. Serra, University lecturers
AbstractResearch colloquium
ContentResearch seminar in Analysis