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H型群上的平均值公式及唯一延拓性 被引量：1

Mean Value Formulas and Unique Continuation on Groups of Heisenberg Type
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摘要 本文求得了H型群上次Laplace算子的基本解,并以此为基础,给出了平均值公式、Hardy型不等式、不确定原理及唯一延拓性． A fundamental solution of the Sub-Laplacian on groups of Heisenberg type is given. On this basis, the mean value formulas, Hardy type inequality, uncertainty principle and unique continuation are established.
作者 韩军强
机构地区 西北工业大学应用数学系
出处 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2007年第2期328-338,共11页 数学研究与评论（英文版）
基金 国家自然科学基金(10371099).
关键词 H型群 基本解 平均值公式 唯一延拓性 group of Heisenberg type fundamental solution mean value formula unique continuation
分类号 O152.5 [理学—基础数学]
  • 相关文献

参考文献8

  • 1KAPLAN K.Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms[J].Trans.Amer.Math.Soc.,1980,258(1):147-153.
  • 2GAROFALO N,VASSILEV D.Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type[J].Duke Math.J.,2001,106(3):411-448.
  • 3FEDERER H.Geometric Measure Theory[M].Springer-Verlag New York Inc.,New York 1969.
  • 4CAPOGNA L,DANIELLI D,GAROFALO N.Capacitary estimates and the local behavior of solutions of nonlinear subelliptic equations[J].Amer.J.Math.,1996,118(6):1153-1196.
  • 5HEINONEN J,HOLOPAINEN I.Quasiregular maps on Carnot groups[J].J.Geom.Anal.,1997,7(1):109-148.
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  • 7GAROFALO N,LANCONELLI E.Frequency functions on the Heisenberg group,the uncertainty principle and unique continuation[J].Ann.Inst.Fourier (Grenoble),1990,40(2):313-356.
  • 8韩军强,钮鹏程,韩亚洲.Heisenberg型群上的几类Hardy型不等式[J].系统科学与数学,2005,25(5):588-598. 被引量：2

二级参考文献8

  • 1Kaplan A. Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms. Trans. Amer. Math. Soc, 1980, 258: 147-153.
  • 2Garofalo N and Lanconelli E. Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation. Ann. Inst. Fourier, Grenoble, 1990, 40(2): 313-356.
  • 3Niu P, Zhang H and Wang Y. Hardy type and Rellich type inequalities on the Heisenberg group.Proc. Amer. Math. Soc, 2001, 129(12): 3623-3630.
  • 4Garofalo N and Vassilev D. Regularity near the characteristic set in the non-linear Dirichlet problem and conformal geometry of sub-Laplacian on Carnot groups. Math. Ann, 2000, 318: 453-516.
  • 5Garofalo N and Vassilev D. Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type. Duke Mathematical Journal, 2001, 106(3): 411-448.
  • 6Capogna L, Danielli D and Garofalo N. Capacitary estimates and the local behavior of solutions of nonlinear subelliptic equations. Amer. J. Math, 1997, 118: 1153-1196.
  • 7Hormander L. Hypoelliptic second order differential equations. Acta Math, 1967, 119: 147-171.
  • 8Davies E B. Spectral Theory and Differential Operators. Cambridge Univ. Press, Cambridge,UK, 1996.

共引文献1

同被引文献6

  • 1KAPLAN A. Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms [J]. Trans Amer Math Soc, 1980, 258(1):147-153.
  • 2KAPLAN A. On the geometry of groups of Heisenberg type [J]. Bull London Math Soc, 1983, 15(1): 35-42.
  • 3BAHOUIR H. Non prolongment unique des solutions d'operatteurs [J]. Ann Inst. Fourier Grenable, 1986, 36(4): 137-155.
  • 4PAN Y. Unique continuation for Schrodinger operators with singular potential [J]. Comm in PDE, 1992, 17(5): 953-965.
  • 5韩静,戴绍虞,潘一飞.关于Heisenberg群上次Laplace算子的唯一延拓性[J].系统科学与数学,2008,28(1):99-106. 被引量：5
  • 6张慧清,钮鹏程,王胜军.Heisenberg群上次Laplace算子的Carleman型估计与唯一延拓性[J].系统科学与数学,2003,23(1):51-57. 被引量：6

引证文献1

Journal of Mathematical Research and Exposition
2007年 第2期

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