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Nontrivial solutions for a class of non-divergence equations on polarizable carnot group

  • Liu Haifeng
  • Niu Pencheng
Article

Abstract

Some new properties of polarizable Carnot group are given. By choosing a proper constant a nontrivial solution of a class of non-divergence Dirichlet problem on the polarizable Carnot group is constructed. Thus the multi-solution property of corresponding non-homogeneous Dirichlet problem is proved and the best possible of L q norm in the famous Alexandrov-Bakelman-Pucci type estimate is discussed.

MR Subject Classification

35J65 35B45 35H20 

Keywords

Dirichlet problem polarizable Carnot group Alexandrov-Bakelman-Pucci estimate 

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Copyright information

© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities 2006

Authors and Affiliations

  • Liu Haifeng
    • 1
  • Niu Pencheng
    • 1
  1. 1.Dept. of Appl. Math.Northwestern Polytechnical Univ.Xi'anChina

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