Sumários

Sobolev spaces (continued)

15 Novembro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

Sobolev inequalities and embeddings of W^{1,p} spaces in L^q spaces.The scaling argument. 

Regularity: Hölder functions. Continuity of H^s (R^N) functions (using Fourier analysis).

Sobolev spaces

14 Novembro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

Characterization of fractional Sobolev spaces H^s (R^N), by means of the Fourier transform.

An exercise on the extension of linear continuous maps, as applied to Fourier transform (Sheet 5, ex. 5).

Sobolev spaces (II)

12 Novembro 2019, 10:00 • Manuel Duque Pereira Monteiro Marques

Multiplication by a test function. Dense subspaces of W k,p. 

Sobolev spaces and Fourier transforms: characterization of H^k (R^N).

Sobolev spaces (part I)

8 Novembro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

Distributional derivatives which are functions.S

Sobolev spaces W^{k,p}: definitions, examples, norms, properties.

Fourier transform

7 Novembro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

Tempered distributions: Fourier and inverse Fourier transforms, differentiation and product with a smooth function.

Comments on exercises on Fourier transforms (exercise sheet 5).