Sumários
Lesson 17: Sobolev Spaces, part IV
26 Abril 2019, 13:30 • Hugo Tavares
Poincaré's inequality: proof and consequences (equivalent norm in H^1_0(Omega)).
Characterization of H^{-1}(Omega), the dual space of H^1_0(Omega).
Statement of the extension theorem for W^{1,p}(Omega), with Omega a C^1 domain. Proof when Omega is a cube.
Lesson 17: Sobolev Spaces, part III
26 Abril 2019, 12:00 • Hugo Tavares
Sobolev embeddings for general Sobolev Spaces W^{k,p}(R^N). Comments on the case N=1; absolutely continuous functions. Introduction to the spaces W^{k,p}_0(R^N): extension property, Sobolev embeddings. Statement of Poincaré's inequality when Omega is a bounded set.
Lecture 16: Sobolev Spaces, part III
16 Abril 2019, 10:30 • Hugo Tavares
Sobolev embedding for W^{1,p}(R^N) in dimension N>1: statement and proof of the case p<N, statement of the case p=N and p>N (Morrey).
Lecture 15: Sobolev Spaces, part II
12 Abril 2019, 12:00 • Hugo Tavares
Density Theorems for W^{k,p}(R^N).
Characterization of the Sobolev space H^k(R^N) using Fourier Transform.
Lecture 14: Fourier Transform, part III. Sobolev Spaces, part I
9 Abril 2019, 10:30 • Hugo Tavares
The derivative of a temperate distribution is a temperate distribution. A polynomial times a tempered distribution is a tempered distribution. Formulas for derivatives of tempered distributions.
Introduction to the Sobolev Spaces W^{k,p}(Omega): definition, norms, examples, elementary properties.