Sumários
Lesson 16: Sobolev Spaces, part III
24 Abril 2018, 14:00 • 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 15: Sobolev Spaces, part III
20 Abril 2018, 11:00 • 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). Brief notions about Holder continuous functions functios.
Exercise class 8
19 Abril 2018, 11:00 • Hugo Tavares
Fourier Transform: Solution of the exercises 1 and 5 of Exercise Sheet 6.
Lecture 15: Sobolev Spaces, part II
17 Abril 2018, 14:00 • Hugo Tavares
Density Theorems for W^{k,p}(R^N).
Characterization of the Sobolev space H^k(R^N) using Fourier Transform.