Details of MA5213 (Spring 2025)
| Level: 5 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA5213 | Sobolev Spaces: Theory and Applications | Rajib Dutta, Saugata Bandyopadhyay, Shirshendu Chowdhury |
| Syllabus |
|---|
| Distribution Theory and Sobolev Spaces
Distribution Theory: Test function spaces, distributions, calculus on distributions and basic examples. Localization, supports of distributions and local structure of distributions. Convolutions. Fourier transform, tempered distributions and Paley-Weiner Theorems. Fundamental solutions and Malgrange-Ehrenpreis Theorem. Sobolev Spaces: Definition and basic properties. Approximation by smooth functions, traces and extension theorems. Sobolev inequalities and Compactness theorems. Applications to Partial Differential Equations: Second-order elliptic equations, weak solutions, existence of weak solutions, L2-regularity theory, maximum principles and eigen-value problem. |
| Prerequisite |
|---|
| Consent of the Instructor.
2nd year math. Functional Analysis Measure Theory A student not doing the prerequisite courses may be allowed by the instructor. |
| References |
|---|
| Suggested Text/Reference Books:
1. L. C. Evans. Partial Differential Equations. Second Edition, AMS, 2010. 2. L. C. Evans and R. F. Gariepy. Measure Theory and Fine Properties of Functions. CRC Press, 1992. 3. D. Gilbarg and N. Trudinger. Elliptic Partial Differential Equations of Second Order. Second Edition, Springer, 1983. 4. S. Kesavan. Topics in Functional Analysis and Applications. Wiley Eastern Limited, 1989. 5. G. Leoni. A First Course in Sobolev Spaces. AMS, 2009 6. W. Rudin. Functional Analysis (Second Edition). McGraw-Hill, 199. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Elective |
| 3 | IP | 6 | Not Allowed |
| 4 | MP | 2 | Not Allowed |
| 5 | MP | 4 | Elective |
| 6 | MR | 2 | Not Allowed |
| 7 | MR | 4 | Not Allowed |
| 8 | MS | 10 | Elective |
| 9 | MS | 4 | Not Allowed |
| 10 | MS | 6 | Not Allowed |
| 11 | MS | 8 | Not Allowed |
| 12 | RS | 1 | Elective |
| 13 | RS | 2 | Elective |