2020 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Analysis D
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Michiaki Onodera
- Class Format
- Lecture (Zoom)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Fri (Zoom)
- Class
- -
- Course Code
- MTH.C404
- Number of credits
- 100
- Course offered
- 2020
- Offered quarter
- 4Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
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 topics in Analysis C.
Course description and aims
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
- 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/Objectives
| Course schedule | Objectives | |
|---|---|---|
| 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. |
Study advice (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.
Evaluation methods and criteria
Report (100%)
Related courses
- MTH.C403 ： Advanced topics in Analysis C
Prerequisites
Not required