Partielle Differentialgleichungen
Titel auf Englisch: Partial Differential Equations
Lernergebnisse
After successfully completing the module, students have deeper knowledge on Analysis and Complex Analysis. They are familiar with the most important concepts and interrelations of partial differential equations and have competently mastered the various analytic methods to solve partial differential equations. Using topics on partial differential equations as examples, students have gained experience in independent scientific work.
Inhalte
On the functional analytic basis, the classical and weak solution theories for linear elliptic differential equations in n variables shall be treated within this lecture. From the lecture notes below, the following themes will be discussed: Potential theoretic foundations, Dirichlet's problem for the Laplace equation and Perron's method, Schauder's continuity method and the Dirichlet problem in Hölder spaces, Existence of weak solutions and their regularity, Moser's iteration method, Green's function for elliptic differential operators.
Voraussetzungen
Verpflichtende Voraussetzungen
Keine
Prüfungsmodalitäten
- Successful completion of homework
- Written examination, 90 min. OR
- Oral examination, 30 min.
Angeboten in
- MathematicsM.Sc.
Wahlpflichtkomplex: Analysis/Algebra/Combinatorics
- MathematikB.Sc.
Wahlpflichtkomplex: Vertiefung
- PhysikB.Sc.
Wahlpflichtkomplex: Nebenfach
| Studiengang | Abschluss | Wahlpflichtkomplex |
|---|---|---|
| Mathematics | M.Sc. | Analysis/Algebra/Combinatorics |
| Mathematik | B.Sc. | Vertiefung |
| Physik | B.Sc. | Nebenfach |
Literatur und Materialien
Friedrich Sauvigny: Partial Differential Equations 1 & 2, UNIVERSITEXT, Springer-Verlag 2006 (Second edition in preparation 2011/12)
Bewertungen von Studierenden
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