Main subjects of this course are nonlinear functional analysis and its application to elliptic partial differential equations.
Beginning with several fundamental results in (linear) functional analysis applied to linear partial differential equations, we learn fixed point theorems and their applications to nonlinear partial differential equations.
This course is followed by Advanced topics in Analysis F1.
Understanding of the basic theory of nonlinear functional analysis including fixed point theorems and their applications to nonlinear partial differential equations
elliptic partial differential equations, functional analysis, fixed point theorems
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
This is a standard lecture course. Occasionally I will give problems for reports.
|Course schedule||Required learning|
|Class 1||- Functional analysis and Sobolev spaces - Linear elliptic partial differential equations - Differentiable functionals - Fixed point theorems 1 - Fixed point theorems 2 - Other topics||Details will be provided during each class.|
Enough preparation and review if necessary
- K. Masuda, Nonlinear mathematics (in Japanese), Asakura Shoten, 1985.
- L. Nirenberg, Topics in Nonlinear Functional Analysis (Courant Lecture Notes), AMS, 2001.