We discuss the variational mothods for the elliptic partial differential equations, and introduce some important methods such as the mountain pass lemma and concentration compactness principle.
This course follows Advanced topics in Analysis A.
Students are expected to understand the variational methods to show the existence of the solutions of elliptic partial differential equations.
variational methods, elliptic partial differential equations, mountain pass lemma, concentration compactness principle
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Standard lecture course.
Course schedule | Required learning | |
---|---|---|
Class 1 | Euler-Lagrange equation | Details will be provided during each class session. |
Class 2 | Minimizing method | Details will be provided during each class session. |
Class 3 | Constraint | Details will be provided during each class session. |
Class 4 | Mountain pass theory 1 | Details will be provided during each class session. |
Class 5 | Mountain pass theory 2 | Details will be provided during each class session. |
Class 6 | Concentration compactness principle 1 | Details will be provided during each class session. |
Class 7 | Concentration compactness principle 2 | Details will be provided during each class session. |
Class 8 | Monotonicity methods | Details will be provided during each class session. |
None in particular
L. C. Evans, Partial Differential Equations, American Mathematical Society
M. Struwe, Variational methods, Springer-Verlag
Students need to submit a report. Details will be announced during the lecture.
Students are required to have completed Advanced topics in Analysis A (MTH.C401).
None in particular