A Contemporary Course on Elliptic Partial Differential Equations (2024)

Convener(s)

 
Name: Prof. Ali Hyder Prof. Debabrata Karmakar
Mailing Address: TIFR CAM Bangalore TIFR CAM Bangalore
Email: hyder at tifrbng.res.in debabrata at tifrbng.res.in

This workshop aimed to provide an extensive yet concise course on contemporary methods in semi-linear elliptic partial differential equations for Ph.D. students from their second year onwards. The workshop covers the existence theory using variational and topological methods. It also focuses on the qualitative properties of solutions, such as their symmetry and regularity. In this work shop the attendees would have exposure to tools from geometric measure theory and harmonic analysis to study elliptic PDEs. We recommend that applicants have knowledge of basic measure theory, functional analysis, weak solutions to linear elliptic PDEs, and H^2- regularity theory to be eligible for the workshop.

 

Dates: 

Monday, May 20, 2024 - 19:00 to Saturday, June 1, 2024 - 19:00

Venue: 

Venue Address: 

 

Tata Institute of Fundamental Research-Centre For Applicable Mathematics (TIFR-CAM)

 Post Bag No6503,GKVK Post Office Sharada Nagar, Chikkabommasandra Bangalore 560065 Karnataka, India

 

 

 

 

Venue State: 

Venue City: 

PIN: 

560065

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

 

 

Selected Applicants: 

 All the shortlisted applicants have been requested to confirm their participation through email to ncmw-ellipticpde@tifrbng.res.in by 22.04.2024, failing which their selection will stand cancelled.

Sr.n SID Full Name Gender Affiliation Position in College/ University University /Institute M.Sc./M.A. Year of Passing M.Sc./ M.A Ph.D. Degree Date
1 54745 Ms. Anupma Arora Female Birla Institute of Technology and Science Pilani PhD Student Guru Jambheshwar University of Science & Technology Hisar 2019  
2 54775 Mr Harish R Male IIT Delhi PhD Indian Institute of Science Education and Research Thiruvananthapuram 2023  
3 54812 Ms. Suman Kanungo Female Indian Institute of Technology Bhilai PhD Pt. Ravishankar Shukla University, Raipur 2020 25/07/2022
4 54815 Mr. Vivek Sahu Male IIT Kanpur PhD IIT Guwahati 2020  
5 54824 Mr. Karan Rathore Male Visvesvaraya National institute of Technology (VNIT) Nagpur PhD Banaras Hindu University 2022  
6 54837 Mr. Utsav Dewan Male Indian Statistical Institute, Kolkata PhD Student Indian Statistical Institute, Kolkata 2020  
7 54867 Mr. Sanjit Biswas Male Indian Institute of Technology Kanpur PhD student Indian Institute of Technology Kanpur. 2020  
8 54880 Mr. Kshitij Sinha Male Indian Institute of Technology Bombay PhD Indian Institute of Technology Kanpur 2022  
9 54887 Mr. Avas Banerjee Male Indian Institute of Technology, Delhi PhD Indian Institute of Science Education and Research, Thiruvananthapuram 2023  
10 54888 Ms. Sarbani Pramanik Female IISER Thiruvananthapuram PhD IISER Thiruvananthapuram 2023  
11 54899 Mr Amal Das Male IIT BOMBAY Ph.D IIT KANPUR 2022  
12 54903 Mr. Susovan Pramanik Male Harish Chandra Research Institute PhD student Vidyasagar University 2019  
13 54913 Ms. Stuti Das Female Indian Institute of Technology PhD Jadavpur University 2021  
14 54929 Mr. Ashutosh Dixit Male IIT Jodhpur PhD Dr. Hari Singh Gour Vishwavidyalaya (A Central University) Sagar 2022  
15 54940 Mr. Govind Kureel Male IIT Kanpur PhD IIT Bhilai 2022  
16 54942 Mr. Surajit Pal Male IIT Bombay PhD IIT Kanpur 2022 27/07/2023
17 54982 Mr Imran Hussain Male IIT BOMBAY Msc -PHD Dual Degree IIT Bombay Appeared  
18 54992 Ms Asmita Rai Female Indian Institute of Technology (BHU) PhD Udai Pratap College 2019  
19 54997 Mr Dattatreya N N Male Indian Institute of Technology Kanpur PhD Mangalore University 2019  
20 55043 Mr. Uday Sureshkumar Patel Male Harish-Chandra Research Institute SRF Sardar Patel University    
21 55132 Mr. Rohan Manish Didmishe Male Indian Institute of Science Education and Research, Kolkata Int. BS-MS Student(4th Year) Indian Institute of Science Education and Research, Kolkata Appeared  
22 55296 Mr. Atanu Manna Male Indian Institute of Technology Hyderabad PhD Indian Institute of Technology Hyderabad 2021  
23 55518 Ms. Nurun Nesha Female IISER KOLKATA IPhD IISER KOLKATA 2019  
24 55559 Mr. Shammi Malhotra Male IIT Delhi PhD IIT Delhi 2022  
25 55584 Ms. Diksha Gupta Female Indian institute of technology Delhi PhD Indian institute of technology Delhi 2020  
26 55681 Ms Nidhi Nidhi Female Indian Institute of Technology, Delhi PhD student Indian Institute of Technology, Mandi 2021  
27 55789 Mr Sourasish Karmakar Male IISER Kolkata MS Student IISER Kolkata 2024  
28 55852 Mr. Nitin Kumar Maurya Male Indian Institute of Technology(BHU), Varanasi PhD National Institute of Technology, Warangal 2022  
29 55920 Ms. Arshi Vaishnavi Female Indian Institute of Technology (BHU) PhD Banaras Hindu University 2021  
30 54757 Mr. Vikram Yallapa Naik Male Birla Institute of Technology and Science Pilani, Pilani Campus PhD University of Mumbai M.Sc 2019  
Waiting List
1 54821 Mr. Vinayak Mani Tripathi Male Indian Institute of Technology Bhilai PhD Banaras Hindu University 2018  
2 54777 Mr. Ravindra Singh Chauhan Male BITS Pilani, Pilani Campus PhD IIT Bhubaneswar 2019  
3 55679 Mr. Souvik Bhowmick Male National Institute of Technology Calicut PhD University Of Kalyani 2020  
4 55093 Mr. Mohd Ashraf Bhat Male IIT Ropar PhD University of Kashmir 2018  
5 54871 Mr Mohmmadameerraja Allauddin Ansari Male IIT Palakkad PhD Sardar patel University 2020  
6 54843 Mr Swapnil Sanap Male Harish-Chandra Research Institute PhD student Savitribai Phule Pune University 2017  
7 55138 Ms. Anusha Bhattacharya Female Indian Institute of Science Education and Research, Mohali Ph.D. Student Chennai Mathematical Institute, M.Sc. 2020  
8 55708 Ms Uma M R Female Central University of Kerala PhD Central University of Kerala 2022  
9 54979 Mr Sajin Vincent A.W. Male IIT Indore Ph.D University of Kerala 2022  
Local Participants
1 54882 Mr. Sourav Ghosh Male Indian Institute of Science (IISc) Bangalore Integrated PhD Student Indian Institute of Science (IISc)    
2 55099 Mr Rohit Mahato Male Indian Institute of science, Bengaluru Int.phd student Indian Institute of science Appeared  
3 55787 Mr. Sayan Adhikari Male IISc Bangalore PhD IIT Guwahati 2022  
4 55875 Dr. Sushil Singla Male Indian Institute of Science Research Associate Shiv Nadar University 2016 15/03/2022

 

 

 

 

School Short Name: 

accepde

Last Date Application: 

Monday, August 15, 2022

School Type: 

NCMW

Separate faculty form: 

0