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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Onodera Michiaki
- Class Format
- Lecture (ZOOM)
- Media-enhanced courses
- Day/Period(Room No.)
- Fri3-4(Zoom)
- Group
- -
- Course number
- MTH.C403
- Credits
- 1
- Academic year
- 2020
- Offered quarter
- 3Q
- Syllabus updated
- 2020/9/18
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
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.
Student learning outcomes
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 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 | 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. |
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.
Assessment criteria and methods
Repots (100%)
Related courses
- MTH.C404 ： Advanced topics in Analysis D
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Not required
