Applications of current-varifold pair to variational method
| Project/Area Number |
23654057
|
|---|
| Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Hokkaido University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Project Status |
Completed (Fiscal Year 2013)
|
| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
|---|
| Keywords | 変分問題 / 相分離 / 平均曲率流 / 幾何学的測度論 / 極小曲面 / バリフォールド / カレント / 変分法 / 偏微分方程式 / 安定性 |
|---|
| Research Abstract |
I have been studying a mathematical model describing phase separation phenomena for the past 15 years. Through the analysis of such model, I realized the importance of a viewpoint to consider surface orientation and surface measure as a pair. In particular, I obtain such a pair as a limiting object when I consider a singular perturbation problem of mean curvature flow. Using this characteristic, I am able to obtain some existence and regularity theorems. The examples of my theorems are existence and regularity theory of mean curvature flow with transport term (joint work with Keisuke Takasao, in review) and existence theorem and characterization of boundary condition of mean curvature flow on a convex domain with Neumann condition (joint work with Masashi Mizuno, in review).
|
Report
(4 results)
Research Products
(32 results)
