ON UNIQUE CONTINUATION PROPERTIES FOR THE SUB-LAPLACIAN ON |CARNOT GROUPS

doi:10.1016/S0252-9602(10)60171-3

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1776-1784.doi: 10.1016/S0252-9602(10)60171-3

ON UNIQUE CONTINUATION PROPERTIES FOR THE SUB-LAPLACIAN ON |CARNOT GROUPS

钮鹏程¹, 王家林^{1, 2}

1. Department of Applied Mathematics, Northwestern Polytechnical University, |Xi'an 710072, |China

2. College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China

收稿日期:2007-04-11 修回日期:2008-12-30 出版日期:2010-09-20 发布日期:2010-09-20
基金资助:
This work was supported by the National Natural Science Foundation of China (10871157), Research Fund for the Doctoral Program of
Higher Education of China (200806990032), and Keji Chuangxin Jijin of Northwestern Polytechnical University (2007KJ01012).

ON UNIQUE CONTINUATION PROPERTIES FOR THE SUB-LAPLACIAN ON |CARNOT GROUPS

NIU Peng-Cheng¹, WANG Jia-Lin^{1, 2}

1. Department of Applied Mathematics, Northwestern Polytechnical University, |Xi'an 710072, |China

2. College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China

Received:2007-04-11 Revised:2008-12-30 Online:2010-09-20 Published:2010-09-20
Supported by:
This work was supported by the National Natural Science Foundation of China (10871157), Research Fund for the Doctoral Program of
Higher Education of China (200806990032), and Keji Chuangxin Jijin of Northwestern Polytechnical University (2007KJ01012).

摘要/Abstract

摘要：

In this article, authors begin with establishing representation formulas and properties for functions on Carnot groups. Then, some unique
continuation results to solutions of sub-Laplace equations with potentials are proved.

关键词: unique continuation, representation formula, spherical function, Carnot group, sub-Laplacian

Abstract:

Key words: unique continuation, representation formula, spherical function, Carnot group, sub-Laplacian

中图分类号:

35H20

钮鹏程, 王家林. ON UNIQUE CONTINUATION PROPERTIES FOR THE SUB-LAPLACIAN ON |CARNOT GROUPS[J]. 数学物理学报(英文版), 2010, 30(5): 1776-1784.

NIU Peng-Cheng, WANG Jia-Lin. ON UNIQUE CONTINUATION PROPERTIES FOR THE SUB-LAPLACIAN ON |CARNOT GROUPS[J]. Acta mathematica scientia,Series B, 2010, 30(5): 1776-1784.

参考文献

[1] Bahouir H. Non prolongment unique des solutions d'operatteurs. Ann Inst Fourier Grenable, 1986, 36(4): 137--155

[2] Balogh Z M, Tyson J T. Polar coordinates in Carnot groups. Math Z, 2002, 241(4): 697--730

[3] Capogna L, Danielli D, Garofalo N. Capacitary estimates and the local behavior of solutions of nonlinear subelliptic equations. Amer J Math, 1997, 118: 1153--1196

[4] D'Ambrosio L. Hardy type inequalities related to degenerate differential operators. Annali della Scuola Normale Superiore di Pisa, 2005, 4(3): 451--486

[5] Folland G B. Subelliptic estimates and function spaces on nilpotent Lie groups. Ark Mat, 1975, 13(2): 161--207

[6] Folland G B, Stein E M. Hardy Spaces on Homogeneous Groups. Princeton, New Jersy: Princeton University Press, 1982

[7] Gallardo L C. Mouvement brownien et probl\`{e}me de lépine de Lebesgue sur les groupes de Lie nilpotents//Probability Measures on Groups. Lecture Notes in Math, Vol 928. Berlin: Springer, 1981: 96--120

[8] Garofalo N. Unique continuation for a class of elliptic operators which degenerate on a manifold of arbitrary codinension. J Diff Eqs, 1993,
104: 117--146

[9] Garofalo N, Lanconelli E. Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation. Ann Inst Fourier, 1990, 40(2): 313--356

[10] Han J, Dai S Y, Pan Y F. On unique continuation property for the sub-Laplacian in the Heisenberg group. System Science and Mathematics (in Chinese), 2008, 28(1): 99--106

[11] Heinonen J. Calculus on carnot groups//Fall School in Analysis of Report, Vol 68. Jyväskylä: Jyväskylä University, 1994: 1--31

[12] Kaplan A. Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms. Trans Amer Math Soc, 1980,
258: 147--153

[13] Luo X B. Removable singularities theorems for solutions of quasihomogeneous hypoelliptis equations//Proc Conf Partial Differential Equations and their Applications. Singapore : World Scientific, 1999: 200--210

[14] Pan Y F. Unique continuation for Schrodinger operators with singular potential. Comm Part Differ Equa, 1992, 17(5): 953--965

[15] Zhang H Q, Niu P C, Wang S J. Unique continuation property and Carlemn type estimate for the sub-Laplacian on the Heisenberg group. System Science and Mathematics (in Chinese), 2003, 23(1): 51--57

[16] Jin K, Chang Q. Remark on unique continuation of solutions to the Stokes and Navier-Stokes equations. Acta Math Sci, 2005, 25B(4): 594--598

ON UNIQUE CONTINUATION PROPERTIES FOR THE SUB-LAPLACIAN ON |CARNOT GROUPS

ON UNIQUE CONTINUATION PROPERTIES FOR THE SUB-LAPLACIAN ON |CARNOT GROUPS

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 6

Metrics

本文评价

推荐阅读 0

[1]	杜锋, 吴传喜, 李光汉, 夏昌玉. UNIVERSAL INEQUALITIES FOR A HORIZONTAL LAPLACIAN VERSION OF THE CLAMPED PLATE PROBLEM ON CARNOT GROUP[J]. 数学物理学报(英文版), 2017, 37(5): 1536-1544.
[2]	Vagif GULIYEV, Ali AKBULUT, Yagub MAMMADOV. BOUNDEDNESS OF FRACTIONAL MAXIMAL OPERATOR AND THEIR HIGHER ORDER COMMUTATORS IN GENERALIZED MORREY SPACES ON CARNOT GROUPS[J]. 数学物理学报(英文版), 2013, 33(5): 1329-1346.
[3]	连保胜. SOME SHARP RELLICH TYPE INEQUALITIES ON NILPOTENT GROUPS AND APPLICATION[J]. 数学物理学报(英文版), 2013, 33(1): 59-74.
[4]	刘晓东, 张波. INVERSE SCATTERING BY AN INHOMOGENEOUS PENETRABLE OBSTACLE IN A PIECEWISE HOMOGENEOUS MEDIUM[J]. 数学物理学报(英文版), 2012, 32(4): 1281-1297.
[5]	付英, 屈长征. UNIQUE CONTINUATION AND PERSISTENCE PROPERTIES OF SOLUTIONS OF THE 2-COMPONENT DEGASPERIS-PROCESI#br# EQUATIONS[J]. 数学物理学报(英文版), 2012, 32(2): 652-662.
[6]	杨乔华; 张钦. THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU(2,2)/S(U(2)×U(2))[J]. 数学物理学报(英文版), 2007, 27(4): 867-874.