2020 Advanced topics in Analysis D

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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.C404
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 topics 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

  • MTH.C403 : Advanced topics in Analysis C

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Not required

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