 Aims
To introduce the student to the major methods for study of elliptic partial differential equations and to the corresponding Dirichlet problem.
Main themes
Methods of potential theory and Hilbert space methods.
Content and teaching methods
Methods of potential theory :
- Laplace equation - harmonic functions
- Dirichlet problem for the Laplacian operator on a ball
- Dirichlet problem for the Laplacian operator on a bounded domain
- Maximum principle for elliptic second order operators
Hilbert space methods :
- Generalized derivatives, Sobolev spaces, Lax-Milgram lemma
- Non-homogeneous Dirichlet problem for elliptic second order operators
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)
The course INMA 2315 is a mandatory prerequisite. The courses MATH 2111 " Functional analysis " and INMA 2325 " Ordinary differential equations " will be quite helpful.
Other credits in programs
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MAP22
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Deuxième année du programme conduisant au grade d'ingénieur civil en mathématiques appliquées
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(3 credits)
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MAP23
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Troisième année du programme conduisant au grade d'ingénieur civil en mathématiques appliquées
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(3 credits)
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MATH22/G
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Deuxième licence en sciences mathématiques
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(3 credits)
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