2020 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Analysis C
- 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.C403
- Number of credits
- 100
- Course offered
- 2020
- Offered quarter
- 3Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
The main subjects of this course are maximum principles for second order elliptic partial differential equations and its applications, including symmetry results in overdetermined problems and nonlinear elliptic equations.
This course is followed by Advanced topics in Analysis D.
Course description and aims
Understanding of the basic theory of second order elliptic partial differential equations with emphasis on maximum principles
Keywords
elliptic partial differential equations, maximum principles, Perron’s method, method of moving planes
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 | Second order elliptic partial differential equations | Details will be provided during each class session. |
| Class 2 | Maximum principles | Details will be provided during each class session. |
| Class 3 | Existence theorem (Perron’s method) 1 | Details will be provided during each class session. |
| Class 4 | Existence theorem (Perron’s method) 2 | Details will be provided during each class session. |
| Class 5 | Method of moving planes | Details will be provided during each class session. |
| Class 6 | Overdetermined problems | Details will be provided during each class session. |
| Class 7 | Symmetry of solutions | 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.
Evaluation methods and criteria
Repots (100%)
Related courses
- MTH.C404 ： Advanced topics in Analysis D
Prerequisites
Not required