Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master

SUBJECT

Code
Subject
MME1001 Sobolev Spaces and Partial Differential Equations
Section
Semester
Hours: C+S+L
Category
Type
Applied Mathematics
1
2+2+0
speciality
compulsory
Teaching Staff in Charge
Prof. PRECUP Radu, Ph.D.,  r.precupmath.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