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一类一般形式的抛物型Monge-Ampère方程

A Class of General Form Parabolic Monge-Ampère Equation
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摘要 对于Caffarelli-Nirenberg-Spruck提出的一种更一般形式的椭圆型Monge-Ampère算子det(D^2u+σ),讨论与之对应的一种抛物型Monge-Ampère方程第一初边值问题。在一定的结构性条件下,利用连续性方法证明了其古典解的存在惟一性。 For a class of general elliptic Monge-Ampere operators det（D^2u ＋ a） which raised by Caffarelli-Nirenberg-Spruck, the corresponding parabolic Monge-Ampere equation is studied. Under some structural assumptions, the existence and uniqueness of the classical solution to the first boundary-initial value problem for the equation are established by means of a continuation approach.
作者 任长宇 关晋瑞 袁洪君
机构地区 吉林大学数学学院
出处 《数学年刊（A辑）》 CSCD 北大核心 2009年第3期421-432,共12页 Chinese Annals of Mathematics
基金 国家自然科学基金(No.J0630104)资助的项目
关键词 一般形式 完全非线性 MONGE-AMPÈRE方程 General form, Fully nonlinear, Monge-Ampere equation
分类号 O175.26 [理学—基础数学] O175.29 [理学—基础数学]
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参考文献15

  • 1Caffarelli L., Nirenberg L. and Spruck J., The Dirichlet problem for nonlinear secondorder elliptic equations I. Monge-Ampere equation [J], Communications on Pure and Applied Mathematics, 1984, 37:369-402.
  • 2Caffarelli L., Nirenberg L. and Spruck J., The Dirichlet problem for nonlinear secondorder elliptic equations Ⅲ. functions of the eigenvalues of the Hessian [J], Acta Mathematics, 1985, 155:261-304.
  • 3Li Yanyan, Some existence results for fully nonlinear elliptic equations of Monge-Apere type [J], Communications on Pure and Applied Mathematics, 1990, 43(2):233-271.
  • 4Krylov N. V., Nonlinear Elliptic and Parabolic Equations of the Second Order [M], Moscow: Nauka, 1985 (in Russian).
  • 5Krylov N. V., Some new results in the theory of nonlinear elliptic and parabolic equations [C]// Proceedings of the International Congress of Mathematicians (Berkeley, CA, 1986), Providence, RI: Amer. Math. Soc., 1987:1101-1109.
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  • 7Ivochkina N. M. and Ladyzhenskaya O. A., Parabolic equations generated by symmetric functions of the eigenvalues of the Hessian or by the principal curvatures of a surface. Ⅰ. Parabolic Monge-Ampere equations [J], Algebra i Analiz, 1994, 6:141-160 (in Russian).
  • 8Ivochkina N. M. and Ladyzhenskaya O. A., Parabolic equations generated by symmetric functions of the eigenvalues of the Hessian or by the principal curvatures of a surface. Ⅰ. Parabolic Monge-Ampere equations [J], St. Petersburg Math. J., 1995, 6:575-594.
  • 9任长宇,王光烈.某种更一般形式的抛物型Monge-Ampère方程[J].吉林大学学报（理学版）,2006,44(1):30-38. 被引量：4
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二级参考文献7

  • 1Caffarelli L, Nirenberg L, Spruck J. The Dirichlet Problem for Nonlinear Second-order Elliptic Equations Ⅰ Monge Ampere Equation [ J ]. Communications on Pure and Applied Mathematics, 1984, 37 : 369-402.
  • 2Caffarelli L, Nircnberg L, Spruck J. The Dirichlet Problem for Nonlinear Second-order Elliptic Equations Ⅲ Functions of the Eigenvalues of the Hessian [ J ]. Acta Mathematics, 1985, 155 : 261-304.
  • 3Li Y. Some Existence Results for Fully Nonlinear Elliptic Equations of Monge-Ampere Type [ J ]. Communications on Pure and Applied Mathematics, 1990, VLⅢ : 233-271.
  • 4Ivochkina N M, Ladyzhenskaya O A. Parabolic Equations Generated by Symmetric Functions of the Eigenvalues of the Hessian or by the Principal Curvatures of a Surface Ⅰ Parabolic Monge-Ampere Equations[ J ]. Algebrai Analiz, 1994,6(3) : 141-160.
  • 5Lieberman G M. Second Order Parabolic Differential Equations [M]. NJ: World Scientific Publishing Co, 1996.
  • 6Horn R A, Johnson C R. Matrix Analysis [ M]. Cambridge: Cambridge University Press, 1985.
  • 7Gilbarg D, Trudinger N S. Elliptic Partial Differential Equations of Second Order [ M ]. 2nd ed. Grundlehren der Mahtematischen Wissenschaften : Vol. 224. Berlin : Springer-Verlag, 1983.

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数学年刊（A辑）
2009年 第3期

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