Sumários
Lesson 23: Elliptic Problems, part IV. Evolution Problems, part I
21 Maio 2019, 10:30 • Hugo Tavares
Conclusion of the H^2-regularity for ellitpic problems. Higher interior regularity. Global regularity and application to the study of a 4th order problem.
Evolution Problems: motivations and abstract Cauchy Problem. Preliminaries on functions with values in Banach spaces (continuity, differentiability, integration).
Lesson 22: Elliptic Problems, part III
17 Maio 2019, 12:00 • Hugo Tavares
Regularity theory: introduction and formal motivation. Sobolev spaces and Difference Quotients. Interior H^2 regularity.
Lesson 21: Elliptic Problems, part II
14 Maio 2019, 10:30 • 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).
Lesson 20: Elliptic Problems, part II
10 Maio 2019, 12:00 • 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.