2000 Fiscal Year Annual Research Report

偏微分方程式,変分問題,逆問題の解の総合的研究

Research Project

Project/Area Number	11640175
Research Institution	TOKYO METROPOLITAN UNIVERSITY
Principal Investigator	倉田和浩東京都立大学, 理学研究科, 助教授 (10186489)
Co-Investigator(Kenkyū-buntansha)	村田実東京工業大学, 理工学研究科, 教授 (50087079) 酒井良東京都立大学, 理学研究科, 教授 (70016129) 望月清東京都立大学, 理学研究科, 教授 (80026773) 田中和永早稲田大学, 理工学部, 教授 (20188288) 神保秀一北海道大学, 理学研究科, 教授 (80201565)
Keywords	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 / ギンツブルグ-ランダウ方程式 / 非線形楕円型方程式 / ガウス曲率流 / Strum-Liouville作用素
Research Abstract	1.倉田は次の研究を行なった。 (1)係数がなめらかでない適当なクラスに属する場合の磁場シュレヂンガー作用素の基本解の3階微分までの評価を与え、関連する作用素のCalderon-Zygmund性を示した。また、磁場シュレヂンガー作用素の熱核の評価の研究を行なった。 (2)いくつかの楕円型作用素のDirichlet第一固有値に関する最小化問題の研究で、対称性の破れなどの現象を発見し、その最小解に付随する自由境界の滑らかさや形状を研究した。また、形状を球に制限しての最適化問題を論じ、いくつかの場合にその最適位置を決定した。 2.分担者の神保は、ギンツブルグ-ランダウ方程式の非自明な安定解の存在について研究し、田中は非線形楕円型方程式-Δu+u=u^Pの摂動に関する不連続な解の振舞いを研究した。村田はユークリッド空間内の非有界領域や非コンパクトRiemann多様体上の二階楕円型および放物型方程式の正値解の構造を研究した。 3.石井は、ガウス曲率流に対する幾何学的近似法の収束を示し、さらにFireyによる石の摩耗の数学モデルを一般化し、曲率が必ずしも凸でない場合に対するガウス曲率流の一般化の存在と一意性を示した。望月は、一般化されたKPP-方程式の解の爆発や漸近挙動の研究およびSturm-Liouville型作用素の内部データからのスペクトル逆問題の研究を行ない、酒井は、2次元の場合に、多面体の外部で同じポテンシャルを形成する細い台を持つ測度が存在するための条件を決定した。

Research Products

(19 results)

All Other

All Publications (19 results)

[Publications] Kazuhiro Kurata: "On Doubling Property for Non-Negative Weak Solutions of Elliptic and Parabolic PDE"Israel J.Math.. 115. 285-302 (2000)
[Publications] Kazuhiro Kurata: "Existence and semi-classical limit of the least energy solution to a nonlinear Schrodinger equolionowith electromagnetic fields"Nonlinca Analysis. 41. 763-778 (2000)
[Publications] K.Kurata (with S.Sugano): "Fundamental Solution, eigenvalne a symptotics and egen function function of degenerate elliptic operators with positive positive potential"Studia Math.. 138(2). 101-119 (2000)
[Publications] K.Karata (with S.Sugano): "Estimates of Fundamental Solution for the magnetic schuidinges operators and their applications"Tohohu Math.J.. 52. 367-382 (2000)
[Publications] Kaguhiro Kurata: "A Remark on finiteness of the Lower Spectrum of uniformly elliptic operators with singular potential"Intergral Eq.and Operator Theory. 36. 212-219 (2000)
[Publications] Kaguhiro Kurata: "Standing wave solution for the Plane Chem-Simono gavged nonlinear Schrodinger equation with and external elrctromagnetic field"J.Korean Math.Soc.. 37. 977-989 (2000)
[Publications] K.Kurata (with S.Chanillo,D.Griesen,M.Iwai,I.Ohmshi): "Symmetry breaking and Other Phencmena in the Optimization of eigenvalues for composite Membranes"Comm.Math.Phys.. 214. 315-337 (2000)
[Publications] K.Kurata (with S.Chanillo,D.Gvieses): "The free boundary Problem in the optimization of composite membranes "Contemporary Math.. 268. 61-81 (2000)
[Publications] Hitoshi Ishii: "Gauss curvatine flow and its approximation"in "Free boundary problems : theory and application II (C Riba,1999), Gakko tosho. 14. 198-206 (2000)
[Publications] H.Ishii (with S.Koike): "On ε-optimal controls for state conetraint problems"Ann Inst.H.Poincase Anal.NonLineatre. 17. 473-502 (2000)
[Publications] K.Mochizahi (with J.Trocshin): "Inverse problem for Interior spectral data of the Sturm-Liouville operator"Inverse Problems. (to appear).
[Publications] K.Mochizuhi (with I.A.Shishmakev): "Large time asymptotics of small solutions to genenalized Kolmogorov-Petrovskii-Piskunov equation"Funkcialy Ekvacioj. (to appear).
[Publications] M.Murata (with K.Ishige): "Uniqueneis of nonnegative solutions of the Canduy problem for parabolic equations on mamtolds or domains"Ann.Scuda Normale Sup.Pisa. (to appear).
[Publications] K.Tanaka (with P.Felmen): "Scattering solutions for plane singular hami Honian systems via minimization"Adv.DiH.Eq.. 5. 1519-1544 (2000)
[Publications] K.Tanaka (with S.Adachi): "Fous positive solutions for the semilinear linear elliptic equation : -su+u=a(x)u^p+f(x) in IR^N"Cal.of Vari.and Partial DiH.Eq.. 11. 63-95 (2000)
[Publications] Kazunaga Tanaka: "Paiodic solutions for singular Hamiltonian systems and closed geodesics on non-compact Riemannian manifolds"Ann.Inst.H.Poincaie Anal.Nan Lineaire. 17. 1-33 (2000)
[Publications] S.Jimbo (with Y.Morita): "Notes on the limit equation of rortex motion for the Ginzburg-Landau equation with Neumann Condition"Japan J.Indst.Appl.Math.. (to appear).
[Publications] Kunio Hidano: "Small data scattering and bolw-up for a wave equation with a cubic convolution"Funkclalaj Ekvacioj. 43. 559-588 (2000)
[Publications] 田中和永: "非線形問題2"岩波書店. 270 (2000)

2000 Fiscal Year Annual Research Report

偏微分方程式,変分問題,逆問題の解の総合的研究

Principal Investigator

倉田 和浩 東京都立大学, 理学研究科, 助教授 (10186489)

Research Products

[Publications] Kazuhiro Kurata: "On Doubling Property for Non-Negative Weak Solutions of Elliptic and Parabolic PDE"Israel J.Math.. 115. 285-302 (2000)

[Publications] Kazuhiro Kurata: "Existence and semi-classical limit of the least energy solution to a nonlinear Schrodinger equolionowith electromagnetic fields"Nonlinca Analysis. 41. 763-778 (2000)

[Publications] K.Kurata (with S.Sugano): "Fundamental Solution, eigenvalne a symptotics and egen function function of degenerate elliptic operators with positive positive potential"Studia Math.. 138(2). 101-119 (2000)

[Publications] K.Karata (with S.Sugano): "Estimates of Fundamental Solution for the magnetic schuidinges operators and their applications"Tohohu Math.J.. 52. 367-382 (2000)

[Publications] Kaguhiro Kurata: "A Remark on finiteness of the Lower Spectrum of uniformly elliptic operators with singular potential"Intergral Eq.and Operator Theory. 36. 212-219 (2000)

[Publications] Kaguhiro Kurata: "Standing wave solution for the Plane Chem-Simono gavged nonlinear Schrodinger equation with and external elrctromagnetic field"J.Korean Math.Soc.. 37. 977-989 (2000)

[Publications] K.Kurata (with S.Chanillo,D.Griesen,M.Iwai,I.Ohmshi): "Symmetry breaking and Other Phencmena in the Optimization of eigenvalues for composite Membranes"Comm.Math.Phys.. 214. 315-337 (2000)

[Publications] K.Kurata (with S.Chanillo,D.Gvieses): "The free boundary Problem in the optimization of composite membranes "Contemporary Math.. 268. 61-81 (2000)

[Publications] Hitoshi Ishii: "Gauss curvatine flow and its approximation"in "Free boundary problems : theory and application II (C Riba,1999), Gakko tosho. 14. 198-206 (2000)

[Publications] H.Ishii (with S.Koike): "On ε-optimal controls for state conetraint problems"Ann Inst.H.Poincase Anal.NonLineatre. 17. 473-502 (2000)

[Publications] K.Mochizahi (with J.Trocshin): "Inverse problem for Interior spectral data of the Sturm-Liouville operator"Inverse Problems. (to appear).

[Publications] K.Mochizuhi (with I.A.Shishmakev): "Large time asymptotics of small solutions to genenalized Kolmogorov-Petrovskii-Piskunov equation"Funkcialy Ekvacioj. (to appear).

[Publications] M.Murata (with K.Ishige): "Uniqueneis of nonnegative solutions of the Canduy problem for parabolic equations on mamtolds or domains"Ann.Scuda Normale Sup.Pisa. (to appear).

[Publications] K.Tanaka (with P.Felmen): "Scattering solutions for plane singular hami Honian systems via minimization"Adv.DiH.Eq.. 5. 1519-1544 (2000)

[Publications] K.Tanaka (with S.Adachi): "Fous positive solutions for the semilinear linear elliptic equation : -su+u=a(x)u^p+f(x) in IR^N"Cal.of Vari.and Partial DiH.Eq.. 11. 63-95 (2000)

[Publications] Kazunaga Tanaka: "Paiodic solutions for singular Hamiltonian systems and closed geodesics on non-compact Riemannian manifolds"Ann.Inst.H.Poincaie Anal.Nan Lineaire. 17. 1-33 (2000)

[Publications] S.Jimbo (with Y.Morita): "Notes on the limit equation of rortex motion for the Ginzburg-Landau equation with Neumann Condition"Japan J.Indst.Appl.Math.. (to appear).

[Publications] Kunio Hidano: "Small data scattering and bolw-up for a wave equation with a cubic convolution"Funkclalaj Ekvacioj. 43. 559-588 (2000)

[Publications] 田中和永: "非線形問題2"岩波書店. 270 (2000)

倉田和浩東京都立大学, 理学研究科, 助教授 (10186489)