UCL - Partial differential equations : Poisson and Laplace equations

[MAT2130]

[30h + 30h] 5 credits

This course is taught in the 1st semester.

Teacher(s): Michel Willem

Language: French

Level: Second

Aims
Main themes
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Aims

The student will have to master elementary facts about the Laplace and Poisson equations, in particular explicit construction of solutions as well as qualitative properties in connection with the maximum principle.

Main themes

The main topics are : fundamental solutions and Green functions, harmonic and subharmonic functions, the Dirichlet principle, decomposition of L2 in eigenfunctions of the Laplace operator, Hilbert space methods, maximum principle, regularity of weak solutions and removable singularities.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Precursorycourses Functional Analysis/Complex Analysis/ Analysis III
Evaluation Examination
Support Dautray-Lions, "L'opérateur de Laplace", is a thorough treatment of the subject
Teaching team Exercises