ADVANCED TOPICS IN ANALYSIS (Sobolev Spaces and Interpolation) (Spring 2010)
Tuesday, 9:30-11:20, N. Masmoudi (spring), in room 512
Prerequisite: real variables and some basic knowledge of PDE and functional analysis.
Sobolev spaces are one of the main tools used in partial differential equations. This course will aim to:
(1) describe basic properties of these spaces (embedding theorems, traces, etc.)
(2) study some cases with non smooth domains (corner singularity or cusp), as well as weighted Sobolev spaces;
(3) study some Hardy inequalities;
(4) Introduce interpolation theory and define more spaces.
Text: An introduction to Sobolev Spaces and Interpolation Spaces, L. Tartar.
Grading: this course will be graded as a seminar course.