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

Luís Manuel Trabucho de Campos

Hours

Weekly - 4

Total - 14

Teaching language

Português

Prerequisites

Background in Functional Analysis and Differential Equations.

Bibliography

  1. L.C. Evans, Partial Differential Equations. American Mathematical Society.
  2. H. Brezis, Analyse Fonctionnelle: théorie et applications. Masson.
  3. D. Gilbarg & N. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer.
  4. 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

Programs

Programs where the course is taught: