Sumários
Lesson no. 26: Evolution Problems, part IV
31 Maio 2019, 12:00 • Hugo Tavares
The Hille-Yosida theorem (conclusion). Applications to the heat and wave equation.
Lesson no. 25: Evolution Problems, part III
28 Maio 2019, 10:30 • Hugo Tavares
The abstract Cauchy problem. The resolvent. Hille-Yosida theorem and Yosida approximation
Lesson 24: Evolution Problems, part II
24 Maio 2019, 12:00 • Hugo Tavares
Evolution Problems: the case of bounded operators (the exponential).Definition of semigroup; contraction semigroups. The infinitesimal operator of a semigroup: differentiable properties, general properties.
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.