MP1 Analytic Methods in PDEs

Course syllabus

The main object of this course is to introduce several fundamental techniques of analysis for the study of partial differential equations. The topic will include Fourier analysis, distributions, differential operators, (pseudo-differential operators). There will be a review of Sobolev spaces, embedding theorems, potentials. [We will apply it to study L2 properties, almost orthogonality, and the regularity of wave (hyperbolic) equations as well as elliptic and parabolic equations.]

Examples & Problem 2015

P.1 ; P.2; P.3; P.4 ; P.5; P.6


Some Books

Walter A. Strauss, Partial Differential Equations: An Introduction

Gerald B. Folland, Introduction to Partial Differential Equations

Lawrence C. Evans, Partial Differential Equations

Fritz John, Partial Differential Equations

Michael E. Taylor, Partial Differential Equations


Gerald B. Folland, Fourier Analysis and Its Applications

Elliott H. Lieb and Michael Loss, Analysis.


Some Books & Lecture Notes On Line

G. Holzegel PDEs Lecture Notes

G. Seregin Functional Analytic Methods for PDEs

Terence Tao Nonlinear dispersive equations: local and global analysis

PDE Books Online


Analysis & PDE