AIS - Elliptic and Parabolic PDEs

Speakers and Syllabus

 

Name of the Speaker with affiliation No. of Lectures Detailed Syllabus
Kunnath Sandeep TIFR-CAM, Bangalore 6 Sobolev spaces, definitions, examples, approximation and extension, basic properties, Traces, Sobolev inequalities and compact embeddings.
Debabrata Karmakar TIFR-CAM, Bangalore 6 Existence theory for elliptic PDEs, Fundamental solutions, Greens function, existence and uniqueness of weak solutions, eigenfunctions and Fredholm alternative, maximum principles, Harnack inequality.
Ali Hyder TIFR-CAM, Bangalore 6 Elliptic regularity, L^{2} estimate, Schauder estimates, up to the boundary estimates.
Arka Mallick Department of Mathematics, IISc ,Bangalore 6 Bochner integrals, Pettis theorem, Sobolev spaces involving time, time- specific embeddings.
Swarnendu Sil Department of Mathematics, IISc ,Bangalore 6 Existence theory for parabolic PDEs, Heat kernel, existence and uniqueness of weak solutions (Galerkin and Gronwall), maximum principles, Harnack inequality.
Karthik Adimurthi TIFR-CAM, Bangalore 6 Parabolic regularity, L^{2} estimate, Schauder estimates, up to the boundary estimates.

 

References:

  1. Partial Differential Equations by L. C. Evans, Garduate studies in Mathematics, Vol 19, AMS.
  2. Functional Analysis, Sobolev spaces and Partial Differential Equations by Springer, UTX
  3. Elliptic Partial Differential Equations by Q. Han and F. Lin Courant Lecture notes in Mathematics, AMS.
  4. Elliptic Partial Differential Equations of Second order by D. Gilbarg and N. S. Trudinger Classics in Mathematics, vol 224, Springer.
  5. Lectures on elliptic and parabolic equations in Sobolev spaces by N.V. Krylov Garduate studies in Mathematics, Vol 96, AMS.
  6. Lectures on elliptic and parabolic equations in Holder spaces by N.V. Krylov Garduate studies in Mathematics, Vol 12, AMS.
  7. Second order Parabolic Differenial Equations by G. M. Lieberman World Scientific.
  8. Partial Differential Equations of Parabolic Type by A. Friedman Dover books on Mathematics, Dover.

Time Table

Time-Table (with initials of speakers and course associates for entire days of the programme ):

Day Date Lecture 1
(9.30–11.00)		 Tea
(11.00–11.30)		 Lecturer 2
(11.30–1.00)		 Lunch
(1.00–2.30)		 Tutorial 1
(2.30–3.30)		 Tea
(3.30- 4.00)		 Tutorial 2
(4.00-5.00)		 Snacks
5.00-5.30
Mon 19/06/ 2023 KS Tea DK Lunch KS+.. Tea DK+.. Snacks
Tues 20/06/ 2023 KS Tea DK Lunch KS+.. Tea DK+.. Snacks
Wed 21/06/ 2023 KS Tea DK Lunch KS+.. Tea DK+.. Snacks
Thu 22/06/ 2023 KS Tea DK Lunch KS+.. Tea DK+.. Snacks
Fri 23/06/ 2023 KS Tea DK Lunch KS+.. Tea DK+.. Snacks
Sat 24/06/ 2023 KS Tea DK Lunch KS+.. Tea DK+.. Snacks
        SUNDAY : OFF        
Mon 26/06/ 2023 AM Tea SS Lunch AM+.. Tea SS+.. Snacks
Tues 27/06/ 2023 AM Tea SS Lunch AM+.. Tea SS+.. Snacks
Wed 28/06/ 2023 AM Tea SS Lunch AM+.. Tea SS+.. Snacks
Thu 29/06/ 2023 AM Tea SS Lunch AM+.. Tea SS+.. Snacks
Fri 30/06/ 2023 AM Tea SS Lunch AM+.. Tea SS+.. Snacks
Sat 01/07/ 2023 AM Tea SS Lunch AM+.. Tea SS+.. Snacks
        SUNDAY : OFF        
Mon 03/07/ 2023 AH Tea KA Lunch AH+.. Tea KA+.. Snacks
Tues 04/07/ 2023 AH Tea KA Lunch AH+.. Tea KA+.. Snacks
Wed 05/07/ 2023 AH Tea KA Lunch AH+.. Tea KA+.. Snacks
Thu 06/07/ 2023 AH Tea KA Lunch AH+.. Tea KA+.. Snacks
Fri 07/07/ 2023 AH Tea KA Lunch AH+.. Tea KA+.. Snacks
Sat 08/07/ 2023 AH Tea KA Lunch AH+.. Tea KA+.. Snacks

 AH: Ali Hyder, AM: Arka Mallick, DK: Debabrata Karmakar, KA: Karthik Adimurthi, KS: Kunnath Sandeep,
SS: Swarnendu Sil.

 

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