Study of Solutions to Partial Differential Equations, Variational problems and Inverse. Problems

偏微分方程、变分问题和逆问题的解的研究。

基本信息

批准号：
11640175
负责人：
KURATA Kazuhiro
金额：
$ 1.47万
依托单位：
TOKYO METROPOLITAN UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640175/
关键词：
magnetic Schrodinger operator Heat Kernel Dirichlet first eigenvalue Ginzburg-Landau equation nonlinear elliptic equation Parabolic equation Gauss curvature flow spectral inverse problem 磁場シュレディンガー作用素 Calderon-zygmund性最適化問題自由境界 S

项目摘要

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.

1。Kurata研究了以下内容：（1）对具有非平滑电位的磁性解决方案的基本解决方案的第二和第三个衍生物的估计，以及某些操作员的Calderon-Zygmund属性。（2）估计磁性schrodinger操作员的热孔的估计值。我们发现某些对称域的最佳配置的对称性现象。我们还研究了与最佳配置相关的自由边界的规律性2。 Jimbo研究了稳定的非固定溶液对金茨堡 - 兰道方程的不存在，并具有磁效应3。田中在非线性精神分子方程式 - ΔU+u = u^p.4的扰动下进行了解决方案的不连续现象。 Murata研究了在非紧密的Riemannian歧管上，对椭圆形和抛物线方程的阳性溶液的结构。5。 Mochizuki研究了kpp方程解决方案的爆破和不对称行为，而跨频谱问题则是内部数据的sturm-liouville操作员的逆频谱问题。6。 ISHII显示了高斯曲率流的几何近似方法的收敛。7。 Sakai研究了在二维情况下具有良好支持的度量的存在状况，并在多边形外产生相同的潜力。