AIS - Geometric measure theory and PDE (2019)
Speakers and Syllabus
Name of the Speakers with their affiliation. |
No. of Lectures |
Detailed Syllabus |
S. Kesavan |
6 |
Rademacher’s theorem on the differentiability of Lipschitz maps from R^n to R^m, Area formula, Change of variable formula, Applications: Length of a curve, surface area, volume |
Mythily Ramaswamy |
6 |
Test functions and Distributions, weak solutions of elliptic problems, Lax-Milgram Theorem, regularity of weak solution, Maximum Principles, Eigenvalue problems. |
Senthil Raani |
6 |
Review of Basic measure theory, Radon-Nikodym theorem, Lebesgue-Besicovitch differentiation theorem. Hausdorff measures, Isodiametric inequality. |
Anoop/ Sarath |
6 |
Sobolev spaces, Extension theorems, embedding theorems, Compact embeddings, Trace theory. |
References:
- Measure Theory and Fine Properties of Functions- Evans & Gariepy
- Topics in Functional Analysis and Applications- S Kesavan
- Functional Analysis, Sobolev Spaces and Partial Differential Equations, H. Brezis
- Geometric measure theory, Federer, Herbert.
(Lecture notes from the speakers, if available)
Time Table
Day | Date | Lectue 1 | Tea | Lecture 2 | Lunch | Tutorial | Tea | Tutorial | Snacks |
(9.30– 11.00) | (11 – 11.25) | (11.30– 1.00) | (1-2.25) | (2.30– 3.30) | (3-3.55) | (4.00-5.0 0) | 5.05- 5.30 | ||
Speaker | Speaker & tutors | Speaker & tutors | |||||||
Mon | 3/6/2019 | A | SR | A,S,LS | SR, SB,U | ||||
Tue | 4/6/2019 | A | SR | A,S,LS | SR, SB,U | ||||
Wed | 5/6/2019 | A | SR | A,S,LS | SR, SB,U | ||||
Thu | 6/6/2019 | A | SR | A,S,LS | SR, SB,U | ||||
Fri | 7/6/2019 | A | SR | A,S,LS | SR, SB,U | ||||
Sat | 8/6/2019 | A | SR | A,S,LS | SR, SB,U | ||||
Mon | 10/6/2019 | K | M | K,S,LS | K,SB,U | ||||
Tue | 11/6/2019 | K | M | K,S,LS | K,SB,U | ||||
Wed | 12/6/2019 | K | M | K,S,LS | K,SB,U | ||||
Thu | 13/6/2019 | K | M | K,S,LS | K,SB,U | ||||
Fri | 14/6/2019 | K | M | K,S,LS | K,SB,U | ||||
Sat | 15/6/2019 | K | M | K,S,LS | K,SB,U |
Tutorial Assistants: | |
Name | Affiliation |
Sarath | IIT Palakkad |
Sayani Bera | RamakrishnaMission |
Ujjal Das | IMSc |
Lakshmi Sankar | IIT Palakkad |