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