Advanced Partial Differential Equations – Politecnico di Milano

Argomenti del programma: 1. Sobolev spaces. Definitions of the Hilbert-type spaces and their duals. Traces. Poincaré inequalities. Embedding theorems. Time dependent Sobolev spaces, the Bochner integral. 2. Elliptic equations . Variational formulation of some boundary value problems for equations in divergence form. Lax-Milgram Theorem and analysis of the well posedness. Eigenvalues and eigenfunctions. The Stokes system.