MP1 Analytic Methods in PDEs
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
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Gerald B. Folland, Fourier Analysis and Its Applications
Elliott H. Lieb and Michael Loss, Analysis.
Links
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
Others