This Advanced Instructional School has been postponed.The new date will be intimated soon.
| Convener(s) | ||
| Name: | Prof. K Sandeep | Prof. Imran H Biswas |
| Mailing Address: | TIFR Centre for Applicable mathematics Bangalore. |
TIFR Centre for Applicable mathematics Bangalore. |
| Email: | sandeep at math.tifrbng.res.in | imran at math.tifrbng.res.in |
Please Note: Participants have to arrange for their own travel.
Dates:
Venue:
Venue Address:
TIFR Centre for Applicable Mathematics
Post Bag No. 6503, GKVK Post Office,
Sharada Nagar, Yelahanka New Town
Bangalore 560065
Venue State:
Venue City:
PIN:
Chrono Order:
Syllabus:
Prerequisites : We expect the participants to be comfortable with basic analysis courses like :
- Several variable calculus : Partial derivatives, Differentiability of functions in Rn , first and second derivatives at local maxima and minima, integration by parts.
- Measure theory : Lebesgue measure, integration, convergence theorems, Lp spaces, Cauchy Schwartz and Minkowski inequalities, Fubini-Tonelli theorems, Lebesgue measure in polar coordinates.
- Functional analysis : Banach spaces,Hilbert spaces, Riesz representation theorem, weak and weak star topologies, reflexive spaces and weak compactness of the unit ball, spectrum, spectral theorems for compact and compact selfadjoint operators.
|
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
| Dr. Debabrata Karmakar (DK) TIFR CAM, Bangalore. |
6 | Sobolev spaces : Definition and basic properties,Sobolev inequalities and embedding theorems |
| Prof. K Sreenadh ( Ksr) IIT Delhi |
6 | Weak solutions of linear elliptic equations, H2 regularity of weak solutions, Weak and strong maximum principle for elliptic equations |
|
Prof. K Sandeep |
6 | Calculus of variation : Notion of derivatives, Euler lagrange equation, minimizers, application to semilinear elliptic equations, Hilbert’s 19th problem and H2 regularity. |
| Dr. Imran Biswas (IB) TIFR CAM, Bangalore. |
5 | Calculus of Variation under sup-norm. Absolutely minimizing Lipschitz extension, Infinity Laplacian. |
| Prof. Adimurthi (A) TIFR CAM, Bangalore. |
5 | P-Laplace equation, Alexanrov maximum principle, Moving plane method and symmetry of solutions of semilinear elliptic equations. |
| Dr. Agnid Banerjee (AB) TIFR CAM, Bangalore |
4 | Non-divergence form PDEs, Krylov-Safanov estimates. |
| Dr. Karthik Adimurthi (KA) TIFR CAM, Bangalore. |
4 | Di-Giorgi-Nash-Moser Theory, elliptic regularity. |
References:
- Partial Differential Equations: Second Edition (Graduate Studies in Mathematics) 2nd Edition , by Lawrence C Evans .
- Functional Analysis, Sobolev Spaces and Partial Differential Equations, by Haim Brezis
- Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian systems, by Michael Struwe.
- Elliptic Partial Differential Equations : Second Edition , by Qing Han and Fanghua Lin
- Aronsson, Gunnar; Crandall, Michael G.; Juutinen, Petri A tour of the theory of absolutely minimizing functions. Bull. Amer. Math. Soc. (N.S.) 41 (2004), no. 4,439–505
Time Table:
|
Day |
Date |
Lecture 1 (9.30–11.00) |
Tea |
Lecturer 2 (11.30–1.00) |
Lunch (1.05–2.25) |
Tutorial (2.30-3.30) |
Tea |
Tutorial (4.00-5:00) |
Snacks |
|
(Speaker’s name) |
(Speaker’s name) |
|
(Speaker’s name) |
(Tutor’s name) |
|||||
| Mon | 29Jun | DK |
T E A |
KSr |
L U N C H |
SH, RD |
T E A |
SH, RD |
S N A C K S |
| Tue | 30Jun | DK |
KSr |
SH, RD |
SH, RD |
||||
| Wed | 1 Jul | DK |
KSr |
SH, RD |
SH, RD |
||||
| Thu | 2 Jul | DK |
KSr |
SH, RD |
SH, RD |
||||
| Fri | 3 Jul | DK |
KSr |
SH, RD |
SH, RD |
||||
| Sat | 4 Jul | DK |
KSr |
SH, RD |
SH, RD |
||||
| Sunday OFF | |||||||||
| Mon | 6 Jul | KSa |
T E A |
KSa |
L U N C H |
SH, VA |
T E A
|
SH, VA |
S N A C K S |
| Tue | 7 Jul | KSa | A | SH, VA | SH, VA | ||||
| Wed | 8 Jul | KSa | A | SH, VA | SH, VA | ||||
| Thu | 9 Jul | IB | KSa | SH, VA | SH, VA | ||||
| Fri | 10 Jul | IB | KSa | SH, VA | SH, VA | ||||
| Sat | 11 Jul | IB | KA | SH, VA | SH, VA | ||||
| Sunday OFF | |||||||||
| Mon | 13 Jul | IB |
T E A |
KA |
L U N C H |
VA ,RD |
T E A
|
VA ,RD |
S N A C K S |
| Tue | 14 Jul | IB | KA | VA ,RD | VA ,RD | ||||
| Wed | 15 Jul | KA | AB | VA ,RD | VA ,RD | ||||
| Thu | 16 Jul | A | AB | VA ,RD | VA ,RD | ||||
| Fri | 17 Jul | A | AB | VA ,RD | VA ,RD | ||||
| Sat | 18 Jul | A | AB | VA ,RD | VA ,RD | ||||
Tutorial Assistants:
|
Sr.. |
Name |
Affiliation |
|
1 |
Ramya Dutta ( RD) |
TIFR CAM, Bangalore |
|
2 |
Saikatul Haque (SH) |
TIFR CAM, Bangalore |
|
3 |
Vedansh Arya (VA) |
TIFR CAM, Bangalore |
Selected Applicants:
To Be Announced