Sumários

Sobolev Spaces: part IV

28 Março 2017, 14:00 • Hugo Tavares

Sobolev embeddings for W^{k,p}(R^N).

Proofs of Sobolev embeddings in the special case p=2 using Fourier transform.

Comments on the special case of dimension N=1.

Introduction to the spaces W_0^{k,p}(R^N).

Sobolev embeddings for W^{1,p}(R^N) in dimension greater than or equal to 2: statemente and proof of the cases p<N, p=N, and statement of Morrey's result for p>N. Brief notions about Hölder continuous functions.

Sobolev spaces: part III

21 Março 2017, 14:00 • Hugo Tavares

Density theorems for W^{k,p}(R^N).

Characterization of the Sobolev space H^k(R^N) using Fourier transform.

Sobolev Spaces: part I

16 Março 2017, 11:00 • Hugo Tavares

Computations of the Fourier Transform of the constant function, and of the Dirac delta.

Introduction to the Sobolev Spaces W^{k,p}(Omega): definition, norms, examples, and elementary properties.

Fourier Transform: part II

14 Março 2017, 14:00 • Hugo Tavares

The Fourier transform and its inverse from the Schwartz space into itself.

Extension to L^2: Plancherel's and Parseval's formulas.

Tempered distributions.