20410518 - AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS

To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study ofÿweak solutions of partial differential equations.

HAUS EMANUELE

teacher profile | teaching materials

Mutuazione: 20410518 AM420 - SPAZI DI SOBOLEV ED EQUAZIONI ALLE DERIVATE PARZIALI in Matematica LM-40 HAUS EMANUELE, FEOLA ROBERTO

Programme

Preliminaries
- Weak topologies and weak convergence, weak lower semi-continuity of the
norm
- L^P spaces: reflexivity, separability, criteria for strong compactness.

Sobolev spaces and variational formulation of boundary value problems in
dimension one
- Motivations
- The Sobolev space W^{1,p} (I)
- The space W^{1,p}_0 (I)
- Some examples of boundary value problems
- Maximum principle

Sobolev spaces and variational formulation of boundary value problems in
dimension N
- Definition and basic properties of the Sobolev spaces W^{1,p} (Omega)
- Extension operators
- Sobolev inequalities
- The space W^{1,p}_0 (Omega)
- Variational formulation of some elliptic boundary value problems
- Existence of weak solutions
- Regularity of weak solutions
- Maximum principle

Core Documentation

Functional analysis, H. Bre'zis

Type of delivery of the course

The course plans lectures.

Attendance

Attendance is not required but strongly suggested.

Type of evaluation

Seminar on a research paper.

FEOLA ROBERTO

teacher profile | teaching materials

Mutuazione: 20410518 AM420 - SPAZI DI SOBOLEV ED EQUAZIONI ALLE DERIVATE PARZIALI in Matematica LM-40 HAUS EMANUELE, FEOLA ROBERTO