| Project/Area Number |
11640175
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | TOKYO METROPOLITAN UNIVERSITY |
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Principal Investigator |
KURATA Kazuhiro Tokyo Metropolitan University, Asso. Prof, 理学研究科, 助教授 (10186489)
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| Co-Investigator(Kenkyū-buntansha) |
MURATA Minoru Tokyo Institute of Technology, Professor, 大学院・理工学研究科, 教授 (50087079)
SAKAI Makoto Tokyo Metropolitan University, Professor, 理学研究科, 教授 (70016129)
MOCHIZUKI Kiyoshi Tokyo Metropolitan University, Professor, 理学研究科, 教授 (80026773)
TANAKA Kazuhaga Waseda University, Professor, 理工学部, 教授 (20188288)
JIMBO Shuichi Hokkaido University, Professor, 大学院・理学研究科, 教授 (80201565)
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| Project Period (FY) |
1999 – 2000
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| Keywords | magnetic Schrodinger operator / Heat Kernel / Dirichlet first eigenvalue / Ginzburg-Landau equation / nonlinear elliptic equation / Parabolic equation / Gauss curvature flow / spectral inverse problem |
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| Research Abstract |
1. Kurata studied the following :
(1) estimates of the second and third derivatives of fundamental solutions to magnetic Schrodinger operators with non-smooth potentials and the Calderon-Zygmund property of certain operators.
(2) estimates of the heat kernel of magnetic Schrodinger operators.
(3) exiestence and further properties of the optimal configuration to several optimization problems for the first Dirichlet eigenvale. Especially, we find a symmetry-breaking pheneomena of the optimal configuration for certain symmetric domains. We also studied the regularity of the free boundary associated with the optimal configuration.
2. Jimbo studied the non-existence of stable non-constant solution to Ginzburg-Landau equation with magnetic effect.
3. Tanaka studied discontinuous phenomena for solutions under the perturbation to nonlinear ellitic equation -Δu+u=u^p.
4. Murata studied the structure of positive solutions to elliptic and parabolic equations of second order on non-compact Riemannian manifolds.
5. Mochizuki studied the blow-up and the asymptotic behavior of solutions to KPP equation and inverse spectrum problem for Sturm-Liouville operator by interior datas.
6. Ishii showed the convergence of geometric approximation method for the Gauss curvature flow.
7. Sakai studied the condition of the existence of a measure which has a fine support and makes the same potential outside the polygon in two-dimensional case.
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