Functional analysis : theory and applications

Lecturer(s): Martine MARION
Course ⋅ 18 hTC ⋅ 14 h


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


Functional analysis, partial differential equations, optimization


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

Learning Outcomes

  • to understand and use the basic functional spaces involved in the study of PDEs
  • to understand ans use different méthods to investigate PDEs


Final mark = 80% Knowledge + 20% Know-how Knowledge N1 = 100% final exam Know-how N2 =100% f continuous assessment