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

1. Kurata研究了以下内容：(1)奇异磁场下薛定谔算子的唯一延拓定理和零集解的估计。(2)一致椭圆算子奇异势下谱的有限性。(3)金兹堡-朗道方程的Liouville型定理和具有磁效应的非线性薛定谔方程的最小能量解的存在性及其分布。(4)由chen - simons - higgs理论导出的非线性椭圆方程非拓扑解的存在性。Jimbo研究了Ginzburg-Landau方程稳定非常解的存在性和零集。Tanaka研究了Hamilton系统，非线性椭圆方程正解的唯一性和非退化性，以及多凸点解的构造。Murata研究了抛物型方程非负解的唯一性。Mochizuki研究了反应扩散系统解的整体存在性和爆破性。7.研究了Hamilton-Jacobi方程的超曲面动力学和均匀化问题。Sakai研究了初始域有角的情况下的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.