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 Lq norm in the famous Alexandrov-Bakelman-Pucci type estimate is discussed.
MR Subject Classification
35J65 35B45 35H20
Dirichlet problem polarizable Carnot group Alexandrov-Bakelman-Pucci estimate
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