EDP modelisation and mathematic analysis

Variational methods, also called energy methods, are a major tool in the study of partial differential equations (PDEs) for linear and nonlinear problems. They rely on estimates of the solutions in well chosen functional spaces and the use of powerful methods borrowed from the theory of functional analysis. The aim of this course is twofold:

• study the tools in analysis underlying these methods,
• apply them to stationary PDEs modeling diffusion processes, called elliptic equations.

Perquisites : it is recommended to have some background on Functional Analysis (at the level of the S8 course on this topic)

• Chapter 1 : Introduction to PDEs
• Chapter 2 : Sobolev spaces
• Chapter 3 : Elliptic equations of second order
• Chapter 4 : Introduction to finite element method