Sumários

Extension and trace operators

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

Extension of functions and applications: new density results and Sobolev embeddings.

The trace operator. Characterization of W^{1,p}_0(Omega) and a Green formula in H^1(Omega).

Not Taught.

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

Incapacidade temporária para o trabalho por estado de doença (vulgo "baixa").

Poincaré's inequality. The space H^{-1}.

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

Poincaré's inequality. Equivalent norm in H^1_0.

The dual space H^{-1}: characterisation, embeddings, example. 

Sobolev spaces

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

Sobolev embedding for W^{1,1}(R^2): complete proof.

Sobolev spaces (continued)

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

Regularity results for H^s (R^N) and W^{1,p}(R).

The spaces W^{k,p}_0 (Omega): definition and special cases (k=0, Omega=R^N).
Extension property. Sobolev embeddings for these spaces.