1999 Fiscal Year Annual Research Report

ポテンシャル解析の横断的研究

Research Project

Project/Area Number	11304008
Research Category	Grant-in-Aid for Scientific Research (A)
Research Institution	Shimane University
Principal Investigator	杉江実郎島根大学, 総合理工学部, 教授 (40196720)
Co-Investigator(Kenkyū-buntansha)	村田實東京工業大学, 理学部, 教授 (50087079) 水田義弘広島大学, 総合科学部, 教授 (00093815) 山崎稀嗣島根大学, 総合理工学部, 教授 (70032935) 福島正俊関西大学, 工学部, 教授 (90015503) 酒井良東京都立大学, 理学部, 教授 (70016129)
Keywords	ポテンシャル / 調和 / 優調和 / 可積分性 / Carleson測度 / 調和測度 / Network / Markov過程
Research Abstract	・境界Harnack原理とMartin境界の決定を一様領域に対して確立した。Mittag-Leffler研究所・研究報告集に掲載、日本数学会誌に発表予定。・John領域上の優調和関数の可積分性の証明。アメリカ数学会誌に掲載。・優調和関数の直線に沿う極限値の存在の証明。イギリス数学会誌に発表予定。以上本研究提案者・相川弘明(島根大学・総合理工学部・教授)を中心とした研究。・擬凸領域に対するBergman-Carleson測度とBloch関数の研究。および、非負曲率を持つ多様体上のHardy空間、Carleson測度の研究。Adv.Studies in Pure Math.等に発表予定。(新井) ・単位球内のBLD関数の境界挙動および、Orlicz族の関数によるRiesポテンシャルの研究。Ann.Acas.Sci.Fenn.等に発表予定。(水田) ・Quadrature領域、調和測度、多面体のポテンシャル論的骨格についての研究。Geometricae Dedicata 等に発表。(酒井) ・Network上のポテンシャル解析、特にHardy不等式、双対性、Kuramochi境界の研究。Optimization等に発表。(山崎) ・Fractal上の確率論主体のポテンシャル解析。特にBrown運動やMarkov過程の研究。Electornic J.Probability等に発表。(福島) ・擬等角性の拡張および正則力学系について研究。Cambridge Univ.Press等から出版発表。(谷口) ・Jorgensenの不等式に関する離散群やJorgensen群の研究を行い、数理解析研究所やContemporary Math.等から発表および発表予定。(佐藤) ・Semilinear elliptic equationの球対称解やポアソン方程式の代用電荷による数値計算の研究を行い、日本数学会誌「数学」等に発表(四ツ谷) ・実力学系のポテンシャル解析への応用として、生態系モデルの極限閉軌道の一意性に関する研究。Nonlinear Anal.やQuart.Appl.Math.に発表および発表予定。(杉江)

Research Products

(32 results)

All Other

All Publications (32 results)

[Publications] H.Aikawa: "Boundary Harnack principle and Martin boundary for a uniform domain"Institut MIttag-Leffler,Report. 2. (1999)
[Publications] H.Aikawa: "Integrability of superharmonic functions in a John domain"Proc.Amer.Math.Soc.. 128. 195-201 (2000)
[Publications] H.Aikawa: "Evaluation of superharmonic functions using limits along lines"Bull.London Math.Soc.. (to appear).
[Publications] H.Aikawa: "Boundary Harnack principle and Martin boundary for a uniform domain"J.Math.Soc.Japan. (to appear).
[Publications] H.Arai: "Bergman-Carleson measueres and Bloch functions on strongly pseudoconvex domains"Reproducing Kernels and Their Applications(Kluwer Acad.Publ.). 21-31 (1999)
[Publications] H.Arai: "Singular elliptic operators related to harmonic analysis and complex analysis of several variables"Trends in Probablity and Related Analysis(World Sci.Publ.). 1-34 (1999)
[Publications] H.Arai: "Hardy spaces,Carleson measures and a gradient estimate for harmonic functions on negatively curved manifolds"Adv.Studies in Pure Math.. (to appear).
[Publications] Y.Mizuta: "Boundary limits of spherical means for BLD abd monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. 26. 45-60 (1999)
[Publications] Y.Mizuta: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. (to appear).
[Publications] Y.Mizuta: "Multiple exponential integrability for Risez potentials of functions in Orlicz classes"Advances in Math.Sci.and Applications. (to appear).
[Publications] B.Gustafsson: "On potential theoretic skeletons of polyhedra"Geometricae Dedicata. 76. 1-30 (1999)
[Publications] M.Sakai: "Linear combinations of harmonic measures and quadrature domains of signed measures with small supports"Proc.Edinburgh Math.Soc.. 42. 433-444 (1999)
[Publications] 生源寺亨浩: "Hardy's inequality on finite networks"Mem.Fac.Sci.Shimane Univ.Ser.B:Mathematical Science. 32. 75-84 (1999)
[Publications] 村上温: "Discrete Kuramochi function"Proc.3rd.Intern.Conference on Difference Equation and Applications. 313-322 (1999)
[Publications] W.Oettli: "Duality theorems on an infinite network"Optimization. (2000)
[Publications] 山崎稀嗣: "Inequalities on networks"RIMS Kokyuroku. 1114. 184-193 (1999)
[Publications] 村上温: "Inequalities on infinite networks"Mem.Fac.Sci.Shimane Univ.Ser.B:Mathematical Science. 33(to appear). (2000)
[Publications] 陳小君: "Verification for existance of solutions of linear complementarity problems"Linear Algebra and Its Applications. (to appear).
[Publications] M.Fukushima: "Large deviations and LIL's for Brownian motions on nested fractals"Osaka J.Math.. 36. 497-537 (1999)
[Publications] M.Fukushima: "On limit theorems for Brownian motions on unbounded fractal sets"Fractal Geometry and Stochastics II'eds.Bandt,Graf,Zahle,Birkhauser. 227-237 (2000)
[Publications] M.Fukushima: "On semimartingale characterizations of functionals of symmetric Markov processes"Electronic J.Probability. 4 Paper 18. 1-32 (1999)
[Publications] Y.Gotoh: "A condition of quasiconformal extendability"Proc.Japan Acad.Ser.A Math.Sci.. 75. 58-60 (1999)
[Publications] H.Sato: "One-parameter families of extreme descrete groups for Jorgensen's infequality"Contemporary Math.. (to appear).
[Publications] H.Sato: "One-parameter families of extreme descrete groups"RIMS Kokyuuroku. 1104. 18-24 (1999)
[Publications] E.Yanagida: "Recent topics on nonlinear partial differential equations-Structure of radial solutions for semilinear elliptic equations-(In Japanese)"Sugaku. 51. 276-290 (1999)
[Publications] 森下博: "代用電荷によるポアソン方程式の数値計算法の改良"情報処理学会論文誌. 40. 3337-3344 (1999)
[Publications] J.Sugie: "Global asymptotic stability of a predator-prey system of Holling type"Nonlinear Analysis. 38. 105-121 (1999)
[Publications] Jitsuro Sugie: "Uniqueness of limit cycles in a predot prey system with Holling-type functional response"Quarterly of Applied Mathematics. (to appear).
[Publications] 相川弘明(編集): "ポテンシャル論とその関連分野(数理解析研究所講究録1116)"京都大学数理解析研究所. (1999)
[Publications] 新井仁之: "フーリエ解析と関数解析学(近刊)"培風館.
[Publications] 水田義弘: "実解析入門-測度・積分・ソボレフ空間"倍風館. (1999)
[Publications] S.Morosawa: "Holomorphic Dynamics"Cambridge Univ.Press. (1999)

1999 Fiscal Year Annual Research Report

ポテンシャル解析の横断的研究

Principal Investigator

杉江 実郎 島根大学, 総合理工学部, 教授 (40196720)

Research Products

[Publications] H.Aikawa: "Boundary Harnack principle and Martin boundary for a uniform domain"Institut MIttag-Leffler,Report. 2. (1999)

[Publications] H.Aikawa: "Integrability of superharmonic functions in a John domain"Proc.Amer.Math.Soc.. 128. 195-201 (2000)

[Publications] H.Aikawa: "Evaluation of superharmonic functions using limits along lines"Bull.London Math.Soc.. (to appear).

[Publications] H.Aikawa: "Boundary Harnack principle and Martin boundary for a uniform domain"J.Math.Soc.Japan. (to appear).

[Publications] H.Arai: "Bergman-Carleson measueres and Bloch functions on strongly pseudoconvex domains"Reproducing Kernels and Their Applications(Kluwer Acad.Publ.). 21-31 (1999)

[Publications] H.Arai: "Singular elliptic operators related to harmonic analysis and complex analysis of several variables"Trends in Probablity and Related Analysis(World Sci.Publ.). 1-34 (1999)

[Publications] H.Arai: "Hardy spaces,Carleson measures and a gradient estimate for harmonic functions on negatively curved manifolds"Adv.Studies in Pure Math.. (to appear).

[Publications] Y.Mizuta: "Boundary limits of spherical means for BLD abd monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. 26. 45-60 (1999)

[Publications] Y.Mizuta: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. (to appear).

[Publications] Y.Mizuta: "Multiple exponential integrability for Risez potentials of functions in Orlicz classes"Advances in Math.Sci.and Applications. (to appear).

[Publications] B.Gustafsson: "On potential theoretic skeletons of polyhedra"Geometricae Dedicata. 76. 1-30 (1999)

[Publications] M.Sakai: "Linear combinations of harmonic measures and quadrature domains of signed measures with small supports"Proc.Edinburgh Math.Soc.. 42. 433-444 (1999)

[Publications] 生源寺亨浩: "Hardy's inequality on finite networks"Mem.Fac.Sci.Shimane Univ.Ser.B:Mathematical Science. 32. 75-84 (1999)

[Publications] 村上温: "Discrete Kuramochi function"Proc.3rd.Intern.Conference on Difference Equation and Applications. 313-322 (1999)

[Publications] W.Oettli: "Duality theorems on an infinite network"Optimization. (2000)

[Publications] 山崎稀嗣: "Inequalities on networks"RIMS Kokyuroku. 1114. 184-193 (1999)

[Publications] 村上温: "Inequalities on infinite networks"Mem.Fac.Sci.Shimane Univ.Ser.B:Mathematical Science. 33(to appear). (2000)

[Publications] 陳小君: "Verification for existance of solutions of linear complementarity problems"Linear Algebra and Its Applications. (to appear).

[Publications] M.Fukushima: "Large deviations and LIL's for Brownian motions on nested fractals"Osaka J.Math.. 36. 497-537 (1999)

[Publications] M.Fukushima: "On limit theorems for Brownian motions on unbounded fractal sets"Fractal Geometry and Stochastics II'eds.Bandt,Graf,Zahle,Birkhauser. 227-237 (2000)

[Publications] M.Fukushima: "On semimartingale characterizations of functionals of symmetric Markov processes"Electronic J.Probability. 4 Paper 18. 1-32 (1999)

[Publications] Y.Gotoh: "A condition of quasiconformal extendability"Proc.Japan Acad.Ser.A Math.Sci.. 75. 58-60 (1999)

[Publications] H.Sato: "One-parameter families of extreme descrete groups for Jorgensen's infequality"Contemporary Math.. (to appear).

[Publications] H.Sato: "One-parameter families of extreme descrete groups"RIMS Kokyuuroku. 1104. 18-24 (1999)

[Publications] E.Yanagida: "Recent topics on nonlinear partial differential equations-Structure of radial solutions for semilinear elliptic equations-(In Japanese)"Sugaku. 51. 276-290 (1999)

[Publications] 森下博: "代用電荷によるポアソン方程式の数値計算法の改良"情報処理学会論文誌. 40. 3337-3344 (1999)

[Publications] J.Sugie: "Global asymptotic stability of a predator-prey system of Holling type"Nonlinear Analysis. 38. 105-121 (1999)

[Publications] Jitsuro Sugie: "Uniqueness of limit cycles in a predot prey system with Holling-type functional response"Quarterly of Applied Mathematics. (to appear).

[Publications] 相川弘明(編集): "ポテンシャル論とその関連分野(数理解析研究所講究録1116)"京都大学数理解析研究所. (1999)

[Publications] 新井仁之: "フーリエ解析と関数解析学(近刊)"培風館.

[Publications] 水田義弘: "実解析入門-測度・積分・ソボレフ空間"倍風館. (1999)

[Publications] S.Morosawa: "Holomorphic Dynamics"Cambridge Univ.Press. (1999)

杉江実郎島根大学, 総合理工学部, 教授 (40196720)