Coursebooks 2017-2018

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Sobolev spaces and elliptic equations

MATH-305

Lecturer(s) :

Nguyên Hoài-Minh

Language:

Français

Résumé

C'est un cours d'introduction aux équations différentielles partielles elliptiques linéaires.

Contenu

1. Harmonic functions. Mean value properties. Fundamental solutions. Green's identities. Maximum principles.
Caccioppoli's inequality.
2. Sobolev spaces. Solobev's inequality, Poincare's inequality, Reillich-Kondrachov's inequality. Trace theorems.
3. Dirichlet problems. Existence and uniqueness of weak solutions. Lax-Milgram's theorem and compactness arguments.
Maximum's principle. A connection with variational method.
4. Neumann problems. Existence and uniqueness of weak solutions. Lax-Milgram's theorem and comptactness
arguments. A connection with variational method.
5. Mixed boundary problems. An example.
6. Separation of variables. Solving Laplace's equations in a ball and in a circular. Three spheres inequality.
7. Laplace equation in unbounded domains.

Compétences requises

Cours prérequis obligatoires

The students are strongly recommended to have sufficiently knowledge on real analysis, theory of
integrations. Having taken a functional analysis course will be an advantage.

Concepts importants à maîtriser

By the end of the course, the student must be able to:
' Apply basic theory to solve several problems in sciences
' Analyze partial differential equations

Méthode d'évaluation

Exam written

 

In the programs

Reference week

 MoTuWeThFr
8-9     
9-10     
10-11     
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     
Under construction
 
      Lecture
      Exercise, TP
      Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German