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

SemesterSpring Semester 2021
LecturersJ. Serra
Periodicitynon-recurring course
Language of instructionEnglish
CommentNumber of participants limited to 12.

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