Functional analysis : theory and applications

For a long time been the study of partial differential equations (PDE) has consisted in the explicit resolution of very few equations. The developments in the theory of Functional Analysis have allowed to investigate much more general problems. This course has two objectives :

• to study functional spaces involved in the study of PDEs
• to investigate linear and nonlinear PDEs

Part I - Linear problems Chapter 1 : Sobolev spaces Chapter 2 : Study of linear elliptic problems Part II - Non linear problems Chapter 3 : Weak topology Chapter 4 : Minimization in infinite dimension and application to PDEs