Heisenberg群上的变分问题

Variational Problem on the Heisenberg Group

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摘要本文研究了Heisenberg群上的变分问题.讨论变分问题的等价形式并运用极小化原理,得到了Heisenberg群上变分问题解的存在性与唯一性.将欧氏空间上变分问题解的存在性与唯一性理论推广到Heisenberg群上. Variational problem on the Heisenberg group （VPHG） is studied in this paper. The uniqueness and existence of the solution of VPHG are proved based on discussion of the equivalence and usage of the minimization principle. It is possible to extend the theory of uniqueness and existence in Euclidean space to the Heisenberg group.

作者毛彦军魏娜

机构地区西北工业大学应用数学系

出处《西安工业大学学报》 CAS 2007年第3期297-299,共3页 Journal of Xi’an Technological University

基金陕西省自然科学基础研究(2006A09)

关键词变分不等方程变分问题 HEISENBERG群存在性唯一性 variational inequalities variational problem heisenberg group existence uniqueness

分类号 O152 [理学—基础数学]

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1Guozhen Lu Department of Mathematics,Wayne State University,Detroit,MI 48202,USA.Polynomials,Higher Order Sobolev Extension Theorems and Interpolation Inequalities on Weighted Folland-Stein Spaces on Stratified Groups[J].Acta Mathematica Sinica,English Series,2000,16(3):405-444. 被引量：10

二级参考文献9

1Alexander Nagel,Elias M. Stein,Stephen Wainger.Balls and metrics defined by vector fields I: Basic properties[J].Acta Mathematica.1985(1)
2Peter W. Jones.Quasiconformal mappings and extendability of functions in sobolev spaces[J].Acta Mathematica.1981(1)
3Sun B,Suo Z.A finite element method for simulating interface motion-Ⅱ.Large shape change due to surface diffusion[].Acta Materialia.1997
4Mullins WW.Theory of thermal grooving[].Journal of Applied Physics.1957
5Nichols FA,Mullins WW.Morphological changes of surface of revolution due to capillarity-induced surface diffusion[].Journal of Applied Physics.1965
6Pan J,Cocks ACF.A numerical technique for the analysis of coupled surface and grain-boundary diffusion[].Acta Materialia.1995
7Mullins WW.Flattening of a nearly plane solid surface due to capillarity[].Journal of Applied Physics.1959
8Cline HE.Shape instabilities of eutectic composites at elevated temperatures[].Acta Metallurgica et Materialia.1971
9Huang Jianming,Yang Wei.Three-dimensional evolution of interfaces under evaporation-condensation kinetics:a finite-element simulation[].Modelling and Simulation in Materials Science and Engineering.1999

共引文献9

1钮鹏程,毛彦军.Heisenberg群上的一阶带权插值不等式[J].西安工业大学学报,2008,28(2):196-198.
2王彦林,赵宁波.非迷向Heisenberg群上的一类带权插值不等式[J].纺织高校基础科学学报,2009,22(3):308-310. 被引量：1
3Ya Zhou HAN,Peng Cheng NIU,Shu Tao ZHANG.On First Order Interpolation Inequalities with Weights on the Heisenberg Group[J].Acta Mathematica Sinica,English Series,2011,27(12):2493-2506.
4白晋彦,崔学伟.带有低阶项的非散度椭圆方程解的二阶导数的高阶可积性(英文)[J].中国科学院研究生院学报,2013,30(3):293-297.
5CUI Xiao-yue,LAM Nguyen,LU Guo-zhen.Characterizations of Sobolev spaces in Euclidean spaces and Heisenberg groups[J].Applied Mathematics(A Journal of Chinese Universities),2013,28(4):531-547. 被引量：3
6Xia LI,Guo Zhen LU,Han Li TANG.Poincaré and Sobolev Inequalities for Vector Fields Satisfying Hrmander's Condition in Variable Exponent Sobolev Spaces[J].Acta Mathematica Sinica,English Series,2015,31(7):1067-1085. 被引量：2
7PEREZ Carlos.L^1→L^q Poincare Inequalities for 0<q<1 Imply Representation Formulas[J].Acta Mathematica Sinica,English Series,2002,18(1):1-20.
8刘莉静,刘晓春.Heisenberg群上一类含有临界Sobolev指数拟线性椭圆方程存在性定理[J].数学物理学报（A辑）,2017,37(3):478-490.
9HAN Yecong,HUANG Tiren,XU Chengdan,ZHU Tingjing.Weighted High Order Poincaré Inequalities on Stratified Lie Groups[J].数学进展,2024,53(5):1071-1083.

1陈凯.次p-线性p-Laplace系统周期解的存在性[J].桂林航天工业高等专科学校学报,2011,16(3):359-361.
2符健,马鑫,张晶.二阶Hamilton系统周期解的存在性[J].佳木斯大学学报（自然科学版）,2009,27(4):590-592.
3肖莉,蒋建初.一类非自治p-Laplace系统的同宿轨道[J].模糊系统与数学,2011,25(4):156-161.
4林振生,李永青.一类p-Laplacian型方程正解的存在性[J].莆田学院学报,2010,17(2):4-8.
5周晓华,尚永兵,曾召利,刘渊声.数理思想在生物医学教学和科研中的应用[J].数理医药学杂志,2014,27(4):486-488.
6赵乃良.具有切向控制的局部四点插值曲线设计方法[J].高校应用数学学报（A辑）,1996(1):91-96.
7秦曾复.高等数学中的外推原理[J].大学数学,1992,13(1):6-10.
8李治平.晶体微观结构的数值计算[J].数学进展,2003,32(3):257-268.

西安工业大学学报

2007年第3期

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Heisenberg群上的变分问题

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