Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT
| MME1001 | Sobolev Spaces and Partial Differential Equations |
| Teaching Staff in Charge |
Assoc.Prof. BUICA Adriana, Ph.D., abuica math.ubbcluj.ro |
| Aims |
|
Basic results from the theory of distributions and Sobolev spaces; modern theiry of partial differential equations. |
| Content |
|
1. Fundamental spaces of the theory of distributions
2. The notion of distribution. Classification. 3. Operations. Derivative. Convolution. 4. The Fourier transform 5. Fundamental solutions. Examples 6. Sobolev spaces 7. The dual of a Sobolev space 8. Sobolev embedding theorem 9. Rellich-Kondrachov compact embedding theorem 10. Variational theory of elliptic equations 11. Semilinear elliptic problems. The Nemytskii operator 12. Existence and uniqueness by the contraction principle 13. Applications of Schauder@s fixed point theorem 14. Application of the Leray-Schauder principle |
| References |
|
1. R. Precup, Lectii de ecuatii cu derivate partiale, Presa Universitara Clujeana, 2004.
2. J. Rauch, Partial Differential Equations, Springer, 1991. 3. H. Brezis, Analyse nonlineaire, Hermann, 1983. 4. M. Taylor, Partial Differential Equations, Springer, 1996.1. L. Schwartz, Theorie des distributions, Hermann, 1959. 5. D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations, Springer, 1983. 6. J.M. Bony, Theorie des distributions et analyse de Fourier, Ecole Polytechnique, Palaiseau, 1997. 7. R.A. Adams, Sobolev Spaces, Academic Press, 1975. |
| Assessment |
|
20% activity to courses and seminaries
20% report 60% written exam |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |