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- Academic unit or major
- Mathematics
- Instructor(s)
- Onodera Michiaki
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Fri3-4(H137)
- Group
- -
- Course number
- ZUA.C334
- Credits
- 1
- Academic year
- 2020
- Offered quarter
- 4Q
- Syllabus updated
- 2020/9/18
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
The main subject of this course is overdetermined problems for elliptic partial differential equations.
We learn its variational structure, a characterization by quadrature identity for harmonic functions, and a dynamical approach.
This course is following Advanced courses in Analysis C.
Student learning outcomes
Understanding of the basic theory of overdetermined problems for elliptic partial differential equations
Keywords
elliptic partial differential equations, overdetermined problems, variational methods, analytic semigroups
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course. Occasionally I will give problems for reports.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Overdetermined problems | Details will be provided during each class session. |
| Class 2 | Variational method and existence theorem 1 | Details will be provided during each class session. |
| Class 3 | Variational method and existence theorem 2 | Details will be provided during each class session. |
| Class 4 | Uniqueness theorem | Details will be provided during each class session. |
| Class 5 | Duality theorem (characterization by quadrature identities) | Details will be provided during each class session. |
| Class 6 | Dynamical approach 1 | Details will be provided during each class session. |
| Class 7 | Dynamical approach 2 | Details will be provided during each class session. |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Not required
Reference books, course materials, etc.
- D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 2001.
- A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhauser, 1995.
Assessment criteria and methods
Report (100%)
Related courses
- ZUA.C333 ： Advanced courses in Analysis C
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Not required
Contact information (e-mail and phone) Notice : Please replace from "[at]" to "@"(half-width character).
onodera[at]math.titech.ac.jp
