2013 Fiscal Year Final Research Report
Applications of current-varifold pair to variational method
| Project/Area Number |
23654057
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Hokkaido University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | 変分問題 / 相分離 / 平均曲率流 / 幾何学的測度論 |
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| 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).
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