Study of Harmonic Analysis, Solutions to Variational Problems and Partial Differential Equa

1. Kurata研究了以下问题：（1）具有奇异磁场的Schrodinger算子的唯一延拓定理和零解集的估计。(2)一致椭圆算子奇异势下谱的有限性。(3)Ginzburg-Landau方程的Liouville型定理和具有磁效应的非线性Schrodinger方程最小能量解的存在性及其轮廓。(4)由Chern-Simons-Higgs理论导出的一类非线性椭圆型方程非拓扑解的存在性2. Jimbo研究了Ginzburg-Landau方程稳定的非常数解的存在性和零集. Tanaka研究了汉密尔顿系统，一类非线性椭圆型方程正解的唯一性和非退化性，以及多凸解的构造. Murata研究了抛物型方程非负解的唯一性. Mochizuki研究了反应扩散方程组解的整体存在性和爆破性.石井研究了超曲面的动力学和Hamilton-Jacobi方程的均匀化. Sakai研究了初始区域有角点情况下的Hale-Shaw流。

1. Kurata studied the following :(1) unique continuation theorem and an estimate of zero set of solutions to Schrodinger operators with singular magnetic fields.(2) finiteness of the lower spectrum of uniformly elliptic operators singular potentials.(3) Liouville type theorem for Ginzburg-Landau equation and existence and its profile of the least energy solution to nonlinear Schrodinger equation with magnetic effect.(4) existence of non-topological solution to a nonlinear elliptic equation arising from Chern-Simons-Higgs theory2. Jimbo studied existence and zero set of stable non-constant solution to Ginzburg-Landau equation.3. Tanaka studied Hamilton system, uniquness and non-degeneracy of positive solution to a nonlinea elliptic equation, and the construction of multi-bump solutions.4. Murata studied uniqueness of non-negative solution to parabolic equation.5. Mochizuki studied global existence and blow-up of solutions to reaction-diffusion systems.6. Ishii studied dynamics of hypersurfaces and homogenization of Hamilton-Jacobi equation.7. Sakai studied Hale-Shaw flow in the case that initial domain has a corner.