AIS - Geometric measure theory and PDE (2019)

Speakers and Syllabus

Name of the Speakers with their affiliation.

No. of Lectures

Detailed Syllabus

S. Kesavan


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


Test functions and Distributions, weak solutions of elliptic problems, Lax-Milgram Theorem, regularity of weak solution, Maximum Principles, Eigenvalue problems.

Senthil Raani


Review of Basic measure theory, Radon-Nikodym theorem, Lebesgue-Besicovitch differentiation theorem. Hausdorff measures, Isodiametric inequality.

Anoop/ Sarath


Sobolev spaces, Extension theorems, embedding theorems, Compact embeddings, Trace theory.


  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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