Sumários

Elliptic Problems: part III

20 Abril 2017, 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).

Regularity theory: introduction and formal motivation. Sobolev spaces and Difference Quotients.

Elliptic Problems: part II

11 Abril 2017, 14:00 • Hugo Tavares

The notion of weak solution in the particular case L=-Delta u + u:

- homogeneous an non-homogenous Dirichlet boundary condition

- Neumann boundary conditions

Sobolev Spaces: part VII; Elliptic Problems: part I

6 Abril 2017, 11:00 • Hugo Tavares

Conclusion of the study of Sobolev Spaces:

- consequences of the Extension theorem;

- the trace operator. Green's theorem in H^1.

Variational Formulation of Elliptic Problems:

- definition of second order elliptic operator in divergence and non-diversion form. The notion of diffusion, transport, and reaction.

- brief comments about several definitions of solution: classical, strong, and distributional solutions.

Sobolev Spaces: Part VI

4 Abril 2017, 14:00 • Hugo Tavares

Definition of C^1 domain. Extension theorem for W^{1,p}(Omega), with Omega a C^1 domain: the case of the cube and half-space. Partition of unity and ideas about the proof in the general case.

Sobolev Spaces: part V

30 Março 2017, 11:00 • Hugo Tavares

Study of the space W_0^{k,p}(Omega): extension property, Sobolev embeddings.

Poincaré's inequality when Omega is a bounded set.

Characterization of H^{-1}(Omega), the dual space of H^1_0(Omega).