Details of MA5214 (Spring 2017)

Level: 5 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA5214 Sobolev Spaces: Theory and Applications Rajib Dutta,
Saugata Bandyopadhyay

(i) Sobolev Spaces: Convolution, Mollifier and Smooth Functions, Weak Derivative, Sobolev Spaces, Approximation by Smooths Functions, Approximations up to the Boundary Extension of Sobolev Functions, Embedding Theorems, Compact Embeddings, Rellich Theorem, Poincare
Inequalities, Traces of Sobolev Functions

(ii) Elliptic PDE (L^2 Theory): Elliptic Equations, Lax-Milgram Theorem, Existence of Weak Solutions, Regularity of Solutions, Maximum Principles, Eigenvalue Problem.

1. *R. A. Adams and J. J. F. Fournier. *Sobolev Spaces. Second edition. Pure and Applied Mathematics (Amsterdam), 140


*Elsevier/Academic Press, Amsterdam,*2003
2. *L. C. Evans. *Partial Differential Equations. Second Edition, AMS, 2010.
3. *L. C. Evans and R. F. Gariepy. *Measure Theory and Fine Properties of Functions. CRC Press, 1992.
4. *D. Gilbarg and N. Trudinger. *Elliptic Partial Differential
Equations of Second Order. Second Edition, Springer, 1983.
5. *S. Kesavan.* Topics in Functional Analysis and Applications. Wiley Eastern Limited, 1989.
6. *G. Leoni.* A First Course in Sobolev Spaces. AMS, 2009

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 2 Not Allowed
2 IP 4 Not Allowed
3 IP 6 Not Allowed
4 MR 2 Not Allowed
5 MR 4 Not Allowed
6 MS 10 Elective
7 RS 1 Elective
8 RS 2 Not Allowed