We discuss the boundary value problem for the elliptic partial differential equations such as the Poisson equation.
Basic and important theorems such as existence of solutions, regularity, and the maximum value principle are introduced.
This course is followed by Advanced topics in Analysis B.
Students are expected to understand the existence, uniqueness and fundamental properties of solutions of elliptic partial differential equations.
Poisson's equation, boundary value problem
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Standard lecture course.
Course schedule | Required learning | |
---|---|---|
Class 1 | Sobolev spaces | Details will be provided during each class session. |
Class 2 | Existence of weak solutions | Details will be provided during each class session. |
Class 3 | Regularity | Details will be provided during each class session. |
Class 4 | Maximum principles | Details will be provided during each class session. |
Class 5 | Harnack's inequality | Details will be provided during each class session. |
Class 6 | Eigenvalues and eigenfunctions | Details will be provided during each class session. |
Class 7 | Supersolution-subsolution method | Details will be provided during each class session. |
Class 8 | Pohozaev's identity and nonexistence of solutions | Details will be provided during each class session. |
None in particular
L. C. Evans, Partial Differential Equations, American Mathematical Society
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag
Students need to submit a report. Details will be announced during the lecture.
Students are required to complete Advanced topics in Analysis A (MTH.C402).
None in particular