Partial Differential Equations
Objectives
Students must become acquainted with the more usual methods
in linear partial differential equations and be aware of its main applications.
General characterization
Code
11590
Credits
6.0
Responsible teacher
Fábio Augusto da Costa Carvalho Chalub
Hours
Weekly - 4
Total - 62
Teaching language
Português
Prerequisites
Background in Functional Analysis and Differential Equations.
Bibliography
- L.C. Evans, Partial Differential Equations. American Mathematical Society.
- H. Brezis, Analyse Fonctionnelle: théorie et applications. Masson.
- D. Gilbarg & N. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer.
- J.-L. Lions & E. Magenes, Nonhomogeneous boundary value problems and Applications, vol.I a III. Springer
Teaching method
Tutorial classes.
Evaluation method
Home work done by the student
Subject matter
1.Introduction to the Theory of Distributions
2. L^p spaces
3. H^m spaces
4. H^m_0 spaces
5. Hahn-Banach theorem
6, Poincaré''''s Inequality
7. Sobolev theorem
8. Variational formulation of an elliptic problem
9. Lax-Milgram theorem
10. Fractional spacews
11. Trace theorem
12. H^(-m) spaces