2020 Advanced topics in Analysis C

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Onodera Michiaki 
Course component(s)
Lecture
Mode of instruction
ZOOM
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
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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

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