1999 年度実績報告書

ポテンシャル解析の横断的研究

研究課題

研究課題/領域番号	11304008
研究種目	基盤研究(A)
研究機関	島根大学
研究代表者	杉江実郎島根大学, 総合理工学部, 教授 (40196720)
研究分担者	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)
キーワード	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
研究概要	・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)

研究成果
(32件)

すべてその他

すべて文献書誌 (32件)

[文献書誌] H.Aikawa: "Boundary Harnack principle and Martin boundary for a uniform domain"Institut MIttag-Leffler,Report. 2. (1999)
[文献書誌] H.Aikawa: "Integrability of superharmonic functions in a John domain"Proc.Amer.Math.Soc.. 128. 195-201 (2000)
[文献書誌] H.Aikawa: "Evaluation of superharmonic functions using limits along lines"Bull.London Math.Soc.. (to appear).
[文献書誌] H.Aikawa: "Boundary Harnack principle and Martin boundary for a uniform domain"J.Math.Soc.Japan. (to appear).
[文献書誌] H.Arai: "Bergman-Carleson measueres and Bloch functions on strongly pseudoconvex domains"Reproducing Kernels and Their Applications(Kluwer Acad.Publ.). 21-31 (1999)
[文献書誌] 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)
[文献書誌] H.Arai: "Hardy spaces,Carleson measures and a gradient estimate for harmonic functions on negatively curved manifolds"Adv.Studies in Pure Math.. (to appear).
[文献書誌] 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)
[文献書誌] Y.Mizuta: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. (to appear).
[文献書誌] Y.Mizuta: "Multiple exponential integrability for Risez potentials of functions in Orlicz classes"Advances in Math.Sci.and Applications. (to appear).
[文献書誌] B.Gustafsson: "On potential theoretic skeletons of polyhedra"Geometricae Dedicata. 76. 1-30 (1999)
[文献書誌] M.Sakai: "Linear combinations of harmonic measures and quadrature domains of signed measures with small supports"Proc.Edinburgh Math.Soc.. 42. 433-444 (1999)
[文献書誌] 生源寺亨浩: "Hardy's inequality on finite networks"Mem.Fac.Sci.Shimane Univ.Ser.B:Mathematical Science. 32. 75-84 (1999)
[文献書誌] 村上温: "Discrete Kuramochi function"Proc.3rd.Intern.Conference on Difference Equation and Applications. 313-322 (1999)
[文献書誌] W.Oettli: "Duality theorems on an infinite network"Optimization. (2000)
[文献書誌] 山崎稀嗣: "Inequalities on networks"RIMS Kokyuroku. 1114. 184-193 (1999)
[文献書誌] 村上温: "Inequalities on infinite networks"Mem.Fac.Sci.Shimane Univ.Ser.B:Mathematical Science. 33(to appear). (2000)
[文献書誌] 陳小君: "Verification for existance of solutions of linear complementarity problems"Linear Algebra and Its Applications. (to appear).
[文献書誌] M.Fukushima: "Large deviations and LIL's for Brownian motions on nested fractals"Osaka J.Math.. 36. 497-537 (1999)
[文献書誌] 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)
[文献書誌] M.Fukushima: "On semimartingale characterizations of functionals of symmetric Markov processes"Electronic J.Probability. 4 Paper 18. 1-32 (1999)
[文献書誌] Y.Gotoh: "A condition of quasiconformal extendability"Proc.Japan Acad.Ser.A Math.Sci.. 75. 58-60 (1999)
[文献書誌] H.Sato: "One-parameter families of extreme descrete groups for Jorgensen's infequality"Contemporary Math.. (to appear).
[文献書誌] H.Sato: "One-parameter families of extreme descrete groups"RIMS Kokyuuroku. 1104. 18-24 (1999)
[文献書誌] E.Yanagida: "Recent topics on nonlinear partial differential equations-Structure of radial solutions for semilinear elliptic equations-(In Japanese)"Sugaku. 51. 276-290 (1999)
[文献書誌] 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)
[文献書誌] J.Sugie: "Global asymptotic stability of a predator-prey system of Holling type"Nonlinear Analysis. 38. 105-121 (1999)
[文献書誌] Jitsuro Sugie: "Uniqueness of limit cycles in a predot prey system with Holling-type functional response"Quarterly of Applied Mathematics. (to appear).
[文献書誌] 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)
[文献書誌] 新井仁之: "フーリエ解析と関数解析学(近刊)"培風館.
[文献書誌] 水田義弘: "実解析入門-測度・積分・ソボレフ空間"倍風館. (1999)
[文献書誌] S.Morosawa: "Holomorphic Dynamics"Cambridge Univ.Press. (1999)

1999 年度 実績報告書

ポテンシャル解析の横断的研究

研究代表者

杉江 実郎 島根大学, 総合理工学部, 教授 (40196720)

研究成果

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

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

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

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

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

[文献書誌] 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)

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

[文献書誌] 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)

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

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

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

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

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

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

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

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

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

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

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

[文献書誌] 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)

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

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

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

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

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

[文献書誌] 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)

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

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

[文献書誌] 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)

[文献書誌] 新井仁之: "フーリエ解析と関数解析学(近刊)"培風館.

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

[文献書誌] S.Morosawa: "Holomorphic Dynamics"Cambridge Univ.Press. (1999)

1999 年度実績報告書

杉江実郎島根大学, 総合理工学部, 教授 (40196720)