Sumários

Variational formulation of elliptic problems

10 Dezembro 2019, 10:00 • Manuel Duque Pereira Monteiro Marques

Regularity of weak solutions: interior regularity and higher interior regularity; 

global or boundary regularity.

Variational formulation of elliptic problems

6 Dezembro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

Homogeneous Dirichlet problem for a general second order elliptic operator: weak formulation.

Lax-Milgram theorem (without a complete proof). 
Existence of the weak solution. 

Weak solutions: examples

5 Dezembro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

Examples of variational formulations for the .equation - Lap(u) +u =f: weak solutions with non-homogeneous Dirichlet boundary condition and for the Neumann problem. 

Variational formulation of elliptic problems (II)

3 Dezembro 2019, 10:00 • Manuel Duque Pereira Monteiro Marques

Weak solution of the model problem with homogeneous Dirichlet boundary condition: 

Dirichlet's principle,energy method, existence by the direct method, and comments.
The corresponding Neumann problem: the definition of weak solution.

Variational formulation of elliptic problems (I)

29 Novembro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

Elliptic problems (second order) in divergence form.

Classical, strong, distributional and weak solutions.
A model problem, with homogeneous Dirichlet boundary condition: 
definition of weak solution;existence, uniqueness and stability, by Riesz representation theorem; Dirichlet's principle (to be continued).