2000 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	水田義弘広島大学, 総合科学部, 教授 (00093815) 相川弘明島根大学, 総合理工学部, 教授 (20137889) 山崎稀嗣島根大学, 総合理工学部, 教授 (70032935) 原惟行大阪府立大学, 工学部, 教授 (20029565) 村田實東京工業大学, 理学部, 教授 (50087079)
キーワード	ポテンシャル / 調和 / 優調和 / ソボレフ関数 / 境界条件 / 放物型 / 正値解 / 非線型
研究概要	● 一様John領域のMartin境界の決定を行い、3次元Sierpinski Gasketに応用した.Mittag-Leffler研究所・研究報告集に掲載.またHolder連続な境界関数に対するDirichlet問題がHolder連続な解を持つための条件を求めた.(相川) ● Orlicz族の関数のRiesポテンシャルの研究の微分可能性とHolder連続性,および重みつきソボレフ関数の境界挙動.(水田,下村,二村) ● Liouvilleの定理とBocherの定理の多調和関数への一般化.(水田,岸,二村) ● タイムラグをもつ2次元線形微分方程式が漸近周期解持つための必要十分条件を求め、応用として非線形項を持つ場合のホップ分岐を調べた.(原) ● 半線形楕円型方程式の正値球対称解を一つの標準形に帰着させ,一見複雑にみえる様々な境界条件も,Dirichlet,Neumann,Robin境界条件と解釈できることを示した.この結果をYanagida-Yotsutaniの全空間での解の構造定理と結びつけることにより,従来の未知であった解の構造を明らかにできると同時に,解の構造の統一的な理解が可能となった.(四ツ谷) ● 分数次の放物型作用素の平均値の原理により帯状領域が特徴づけられることを示した.(鈴木) ● 多様体や領域上の放物型方程式に対するCauchy問題の正の解の一意性を示した.(村田)

研究成果
(27件)

すべてその他

すべて文献書誌 (27件)

[文献書誌] H.Aikawa: "Martin boundary of a fractal domain"Institut Mittag-Leffer, Report. 40. (2000)
[文献書誌] H.Aikawa,S.Gardinder: "Evaluation of superharmonic functions using limits along lines"Bull.London Math.Soc.. 32. 209-213 (2000)
[文献書誌] H.Aikawa: "Boundary Harnack principle and Martin boundary-for a uniform domain"J.Math.Soc.Japan. 53. 119-145 (2001)
[文献書誌] 新井仁之: "実解析,掛谷問題とコロナ問題-日本発の二つの問題-"数理科学. 38. 56-65 (2000)
[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 and T.Shimomura: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad.Sci.Fenn.,Ser.A.I.Math.. 25. 457-465 (2000)
[文献書誌] Y.Mizuta and T.Shimomura: "Differentiability and Holder continuity of Riesz potentials of functions in Orlicz classes"Analysis. 20. 201-223 (2000)
[文献書誌] Y.Mizuta: "Boundary limits of functions in weighted Lebesgue or Sobolev classes"Revue Roumaine Math.Pures Appl.. 45(to appear). (2000)
[文献書誌] T.Futamura,K.Kishi,Y.Mizuta: "A generalization of the Liouville theorem to polyharmonic functions"J.Math.Soc.Japan. 53. 113-118 (2001)
[文献書誌] T.Futamura,K.Kishi,Y.Mizuta: "A generalization of Bocher's theorem for polyharmonic functions (to appear)"Hiroshima Math.J.. 31. (2001)
[文献書誌] T.Futamura and Y.Mizuta: "Existence of functions in weighted Sobolev spaces (to appear)"Nagoya Math.J.. 31. (2001)
[文献書誌] M.Nishio and N.Suzuki: "A charcterzation of strip domains by mean value property for the parabolic operator of order α"New Zealand J of Math.. 29. 47-54 (2000)
[文献書誌] N.Suzuki and N.A.Watson: "A charcterization of heat ball by mean value property for temperatures"Proc.Amer.Math.Soc.. (to appear) .
[文献書誌] Oettli,W.,山崎稀嗣: "Duality theorems on an infinite network"Optimization. 48. 1-15 (2000)
[文献書誌] 村上温,山崎稀嗣: "Inequalities on infinite networks"Mem.Fac.Sci.Shimane Univ.Ser.B : Mathematical Science. 33(to appear) . 47-62 (2000)
[文献書誌] 陳小君,生源寺亨浩,山崎稀嗣: "Verification for existence of solutions of linear complementarity problems"Linear Algebra and Its Applications. (to appear). (2000)
[文献書誌] 谷口雅彦: "整函数の構成:断章"数理解析研究所講究録. 1153. 103-112 (2000)
[文献書誌] E.Fujikawa,H.Shiga and M.Taniguchi: "Discreteness of the mapping class group for Riemann surfaces of infinite analytic type"Proc.of the 2-nd ISAAC Congress. 2000. 1015-1023
[文献書誌] K.Ishige and M.Murata: "Uniqueness of nonnegative solutions of the cauchy problem for parabolic equations on manifolds or domains"Ann.Scuola Normale Sup.Pisa. (to appear).
[文献書誌] H.Morishita,E.Yanagida,S.Yotsutani: "Structural change of solutions for a scalar curvature equation"Differential and Integral Equations. 14(to appear). (2001)
[文献書誌] E.Yanagida,and S.Yotsutani: "A unified approach to the structure of radial solutions for semilinear elliptic problems"JJIAM. 18(to appear). (2001)
[文献書誌] T.Hara,R.Miyazaki,T.Morii: "Asymptotic periodic solutions for linear differential-difference equations with N delays and Hopf bifurcation"Funkcialaj Ekvacioj. 43. 193-212 (2000)
[文献書誌] W.Ma,T.Hara,Y.Takeuchi: "Stability of a 2-dimensional neural network with time delays"Journal of Biological Systems. 8. 177-193 (2000)
[文献書誌] R.Ogita,H.Matsunage,T.Hara: "Asymptotic stability condition for a class of linear delay difference equations of higher order"J.Math.Anal.Appl.. 248. 83-96 (2000)
[文献書誌] S.Sakata and T.Hara: "Dynamics of a linear differential system with piecewise constant argument"Dynam.Contin.Discrete Impuls.Systems. 7. 585-594 (2000)
[文献書誌] 新井仁之: "フーリエ解析と関数解析学"培風館(近刊).

2000 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: "Martin boundary of a fractal domain"Institut Mittag-Leffer, Report. 40. (2000)

[文献書誌] H.Aikawa,S.Gardinder: "Evaluation of superharmonic functions using limits along lines"Bull.London Math.Soc.. 32. 209-213 (2000)

[文献書誌] H.Aikawa: "Boundary Harnack principle and Martin boundary-for a uniform domain"J.Math.Soc.Japan. 53. 119-145 (2001)

[文献書誌] 新井仁之: "実解析,掛谷問題とコロナ問題-日本発の二つの問題-"数理科学. 38. 56-65 (2000)

[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 and T.Shimomura: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad.Sci.Fenn.,Ser.A.I.Math.. 25. 457-465 (2000)

[文献書誌] Y.Mizuta and T.Shimomura: "Differentiability and Holder continuity of Riesz potentials of functions in Orlicz classes"Analysis. 20. 201-223 (2000)

[文献書誌] Y.Mizuta: "Boundary limits of functions in weighted Lebesgue or Sobolev classes"Revue Roumaine Math.Pures Appl.. 45(to appear). (2000)

[文献書誌] T.Futamura,K.Kishi,Y.Mizuta: "A generalization of the Liouville theorem to polyharmonic functions"J.Math.Soc.Japan. 53. 113-118 (2001)

[文献書誌] T.Futamura,K.Kishi,Y.Mizuta: "A generalization of Bocher's theorem for polyharmonic functions (to appear)"Hiroshima Math.J.. 31. (2001)

[文献書誌] T.Futamura and Y.Mizuta: "Existence of functions in weighted Sobolev spaces (to appear)"Nagoya Math.J.. 31. (2001)

[文献書誌] M.Nishio and N.Suzuki: "A charcterzation of strip domains by mean value property for the parabolic operator of order α"New Zealand J of Math.. 29. 47-54 (2000)

[文献書誌] N.Suzuki and N.A.Watson: "A charcterization of heat ball by mean value property for temperatures"Proc.Amer.Math.Soc.. (to appear) .

[文献書誌] Oettli,W.,山崎稀嗣: "Duality theorems on an infinite network"Optimization. 48. 1-15 (2000)

[文献書誌] 村上温,山崎稀嗣: "Inequalities on infinite networks"Mem.Fac.Sci.Shimane Univ.Ser.B : Mathematical Science. 33(to appear) . 47-62 (2000)

[文献書誌] 陳小君,生源寺亨浩,山崎稀嗣: "Verification for existence of solutions of linear complementarity problems"Linear Algebra and Its Applications. (to appear). (2000)

[文献書誌] 谷口雅彦: "整函数の構成:断章"数理解析研究所講究録. 1153. 103-112 (2000)

[文献書誌] E.Fujikawa,H.Shiga and M.Taniguchi: "Discreteness of the mapping class group for Riemann surfaces of infinite analytic type"Proc.of the 2-nd ISAAC Congress. 2000. 1015-1023

[文献書誌] K.Ishige and M.Murata: "Uniqueness of nonnegative solutions of the cauchy problem for parabolic equations on manifolds or domains"Ann.Scuola Normale Sup.Pisa. (to appear).

[文献書誌] H.Morishita,E.Yanagida,S.Yotsutani: "Structural change of solutions for a scalar curvature equation"Differential and Integral Equations. 14(to appear). (2001)

[文献書誌] E.Yanagida,and S.Yotsutani: "A unified approach to the structure of radial solutions for semilinear elliptic problems"JJIAM. 18(to appear). (2001)

[文献書誌] T.Hara,R.Miyazaki,T.Morii: "Asymptotic periodic solutions for linear differential-difference equations with N delays and Hopf bifurcation"Funkcialaj Ekvacioj. 43. 193-212 (2000)

[文献書誌] W.Ma,T.Hara,Y.Takeuchi: "Stability of a 2-dimensional neural network with time delays"Journal of Biological Systems. 8. 177-193 (2000)

[文献書誌] R.Ogita,H.Matsunage,T.Hara: "Asymptotic stability condition for a class of linear delay difference equations of higher order"J.Math.Anal.Appl.. 248. 83-96 (2000)

[文献書誌] S.Sakata and T.Hara: "Dynamics of a linear differential system with piecewise constant argument"Dynam.Contin.Discrete Impuls.Systems. 7. 585-594 (2000)

[文献書誌] 新井仁之: "フーリエ解析と関数解析学"培風館(近刊).

2000 年度実績報告書

杉江実郎島根大学, 総合理工学部, 教授 (40196720)