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Partial differential equations : Poisson and Laplace equations [ LMAT2130 ]


5.0 crédits ECTS  30.0 h + 30.0 h   1q 

Teacher(s) Ponce Augusto ; Van Schaftingen Jean ;
Language French
Place
of the course
Louvain-la-Neuve
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.
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.
Other information 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
Cycle et année
d'étude
> Master [120] in Mathematics
> Master [120] in Physics
> Master [60] in Mathematics
> Master [120] in Mathematical Engineering
> Master [120] in Statistics: General
Faculty or entity
in charge
> MATH


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