Sumários

Exercise class 12

17 Maio 2018, 11:00 • Hugo Tavares

Weak formulation of Elliptic Problems. Riesz vs Lax-Milgram. Possible norms in H^1_0(Omega) with Omega bounded.

Solution of exercises 1a)b) and 2 of Exercise Sheet 8.

Lesson 22: Elliptic Problems, part III

15 Maio 2018, 14:00 • Hugo Tavares

Regularity theory:: introduction and formal motivation. Sobolev spaces and Difference Quotients. Interior H^2 regularity.

Lesson 21: Elliptic Problems, part II

11 Maio 2018, 11:00 • Hugo Tavares

Lax-Milgram's theorem and its application to the existence and uniqueness of weak solutions for a general second order elliptic operator in divergence form (the case of homogeneous Dirichlet boundary conditions).

Exercise class 11

10 Maio 2018, 11:00 • Hugo Tavares

Sobolev Spaces. Solution of exercises 3, 4 and 5 of Exercise Sheet 7.

Lesson 20: Elliptic Problems, part II

8 Maio 2018, 14:00 • Hugo Tavares

Conclusion of the proof of the Dirichlet's principle.

The notion of weak solution for L=-Delta u+u: non homogenous Dirichlet boundary conditions; Neumann boundary conditions.

Motivations for the need of generalizing Riesz's theorem.