401-3350-21L  Classical Theory of Elliptic Partial Differential Equations

SemesterFrühjahrssemester 2021
DozierendeJ. Serra
Periodizitäteinmalige Veranstaltung
KommentarNumber of participants limited to 12.

KurzbeschreibungFollowing 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
LernzielTo 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.)
Inhalt(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
LiteraturElliptic 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
Voraussetzungen / BesonderesAlthough many parts of the book are rather self-contained, it would be advisable to have followed before the bachelor course Functional Analysis II