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- Academic unit or major
- Mathematics
- Instructor(s)
- Tonegawa Yoshihiro Shibata Masataka
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(H201)
- Group
- -
- Course number
- ZUA.C331
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 1Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
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 continuous with Advanced courses in Analysis B.
Student learning outcomes
Students are expected to understand the existence, uniqueness and fundamental properties of solutions of elliptic partial differential equations.
Keywords
Poisson's equation, boundary value problem
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Standard lecture course
Course schedule/Required learning
| 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. |
Textbook(s)
None in particular
Reference books, course materials, etc.
L. C. Evans, Partial Differential Equations, American Mathematical Society
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag
Assessment criteria and methods
Students need to submit a report. Details will be announced during the lecture.
Related courses
- ZUA.C332 ： Advanced courses in Analysis B
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are required to complete Advanced courses in Analysis B (ZUA.C332).
Other
None in particular
