Project/Area Number  09640208 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  TOKYO METROPOLITAN UNIVERSITY 
Principal Investigator 
KURATA Kazuhiro Tokyo Metropolitan Unviersity, Assistant Professor, 理学研究科, 助教授 (10186489)

CoInvestigator(Kenkyūbuntansha) 
TANAKA Kazunaga Waseda University, Assistant Professor, 理工学部, 助教授 (20188288)
JIMBO Shuichi Hokkaido Universirty, Professor, 理学研究科, 教授 (80201565)
MURATA Minoru Tokyo Institute of Technology, Professor, 理工学研究科, 教授 (50087079)
SAKAI Makoto Tokyo Metropolitan Unviersity, Professor, 理学研究科, 教授 (70016129)
MOCHIZUKI Kiyoshi Tokyo Metropolitan Unviersity, Professor, 理学研究科, 教授 (80026773)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥2,200,000 (Direct Cost : ¥2,200,000)
Fiscal Year 1998 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1997 : ¥1,300,000 (Direct Cost : ¥1,300,000)

Keywords  Super conductivity / GinzburgLandau equation / Semclassical limit / Schrodinger operator / spectrum / elliptic equation / variational problem / singular perturbation problem / 超伝導 / GinzburgLandau方程式 / 半古典極限 / Schrodinger作用素 / スペクトル / 楕円型方程式 / 変分問題 / 特異摂動問題 / スペクトエル / Morrey空間 / ハミルトン・ヤコビ方程式 / 一意接続性定理 / ChernSimonsHiggs理論 / スカラー曲率方程式 / FeffermanPhong不等式 / 対称性 
Research Abstract 
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 GinzburgLandau equation and existence and its profile of the least energy solution to nonlinear Schrodinger equation with magnetic effect. (4) existence of nontopological solution to a nonlinear elliptic equation arising from ChernSimonsHiggs theory 2. Jimbo studied existence and zero set of stable nonconstant solution to GinzburgLandau equation. 3. Tanaka studied Hamilton system, uniquness and nondegeneracy of positive solution to a nonlinea elliptic equation, and the construction of multibump solutions. 4. Murata studied uniqueness of nonnegative solution to parabolic equation. 5. Mochizuki studied global existence and blowup of solutions to reactiondiffusion systems. 6. Ishii studied dynamics of hypersurfaces and homogenization of HamiltonJacobi equation. 7. Sakai studied HaleShaw flow in the case that initial domain has a corner.
