NCMW - A Contemporary Course on Elliptic Partial Differential Equations (2024)

Speakers and Syllabus

 

Name of the Speaker with their Affiliation

No. of Lectures

Detailed Syllabus

Imran Biswas, TIFR-CAM

6

Geometric measure theory: Hausdorff measure; One dimensional Hausdorff measure as length, Isodiametric inequality; Lipschitz functions and Radamacher’s theorem, area formula and its consequences.

Debdip Ganguly, IIT Delhi

6

Symmetrization and its applications: The decreasing rearrangement; Schwartz symmetrization; isoperimetric inequality; Polya-Szego inequality and its application to Sobolev inequalities.

S Prashanth, TIFR-CAM

6

Calculus of variations: Fréchet derivative, Direct method in COV; constrained minimizations and applications to elliptic PDEs.

Arka Mallick, IISc Bangalore

6

Degree theory: Brouwer degree and its properties; Leray-Schauder degree; fixed point theorems; application to Leray-Schauder degree to elliptic PDEs.

Swarnendu Sil, IISc Bangalore

6

Singular integrals: Maximal functions; Calderon-Zygmund decomposition, Marcinkiewicz interpolation theorem; L^p-estimates.

K. Sandeep, TIFR-CAM

6

Strong solutions: Schauder theory; method of continuity, De Giorgi- Nash-Moser theory and application to Hilbert’s 19th problem.

 References:

  1. Real Analysis: Measure Theory, Integration, and Hilbert Spaces by Elias M. Stein and Rami Shakarchi.
  2. Analysis (Graduate Studies in Mathematics) by Elliott H. Lieb and Michael Loss.
  3. Symmetrization And Applications: 3 (Series In Analysis) by S Kesavan.
  4. Introduction to the Calculus of Variations by Bernard Dacorogna.
  5. Partial Differential Equations (Graduate Studies in Mathematics) by Lawrence C. Evans.
  6. Nonlinear Functional Analysis by Klaus Deimling
  7. Measure theory and fine properties of functions by Lawrence C. Evans and Ronald F. Gariepy
  8. An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs by Mariano Giaquinta and Luca Martinazzi.
  9. Singular Integrals and Differentiability Properties of Functions by Elias M. Stein.
  10. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals by Elias M. Stein.
  11. Elliptic Partial Differential Equations of Second Order by David Gilbarg and Neil S. Trudinger.
  12. Elliptic Partial Differential Equations by Qing Han and Fanghua Lin. (Lecture notes from the speakers, if available)

 

Names of the tutors with their affiliations:

1. Nisha Singhal, TIFR-CAM
2. Divyansh Agrawal, TIFR-CAM
3. Monideep Ghosh, TIFR-CAM
4. Anirban Das, TIFR-CAM

Speakers
IB: Imran Biswas
DG: Debdip Ganguly
SP: S Prashanth
AM: Arka Mallick
KS: K. Sandeep
SS: Swarnendu Sil

 Tutors
NS: Nisha Singhal
DA: Divyansh Agrawal
MG: Monideep Ghosh
AD: Anirban Das

 

 

Time Table

Week1

Day

Date

Lecture 1

(9.30–11.00)

Tea
(11.05-11.25)

Lecture 2

(11.30–1.00)

Lunch
(1.05–1.55)

Lecture 3

(2.00–3.30)

Tea (3.35-3.55)

Discussion (4.00-5.00)

Snacks (5.05-5.35)

 

 

(name of the speaker)

 

(name of the speaker)

 

(name of the speaker)

 

(Name of the tutor)

 

Mon

20.05.24

IB

 

DG

 

SP

 

IB+NS+DA

 

Tues

21.05.24

IB

 

DG

 

SP

 

DG+NS+DA

 

Wed

22.05.24

IB

 

DG

 

SP

 

SP+NS+DA

 

Thu

23.05.24

IB

 

DG

 

SP

 

IB+NS+DA

 

Fri

24.05.24

IB

 

DG

 

SP

 

DG+NS+DA

 

Sat

25.05.24

IB

 

DG

 

SP

 

SP+NS+DA

 

 Week 2

 

Day

Date

Lecture 1

(9.30–11.00)

Tea
(11.05-11.25)

Lecture 2

(11.30-1.00)

Lunch
(1.05–1.55)

Lecture3

(2.00–3.30)

Tea
(3.35-3.55)

Discussion
(4.00-5.00)

Snacks
5.05-5.35

 

 

(name of the speaker)

 

(name of the speaker)

 

(name of the speaker)

 

(Name of the tutor)

 

Mon

27.05.24

AM

 

KS

 

SS

 

AM+MG+AD

 

Tues

28.05.24

AM

 

KS

 

SS

 

KS+MG+AD

 

Wed

29.05.24

AM

 

KS

 

SS

 

SS+MG+AD

 

Thu

30.05.24

AM

 

KS

 

SS

 

AM+MG+AD

 

Fri

31.05.24

AM

 

KS

 

SS

 

KS+MG+AD

 

Sat

01.06.24

AM

 

KS

 

SS

 

SS+MG+AD

 

 

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