Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (5): 1776-1784.doi: 10.1016/S0252-9602(10)60171-3

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

 NIU Peng-Cheng1, WANG Jia-Lin1, 2   

  1. 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).

Abstract:

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.

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

CLC Number: 

  • 35H20
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