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
of a submanifold, Coarea formula, Applications: Polar coordinates

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:

  1. Measure Theory and Fine Properties of Functions- Evans & Gariepy
  2. Topics in Functional Analysis and Applications- S Kesavan
  3. Functional Analysis, Sobolev Spaces and Partial Differential Equations, H. Brezis
  4. 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
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