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.
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Supported by the National Natural Science Foundation of China (10371099).
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Haifeng, L., Pencheng, N. Nontrivial solutions for a class of non-divergence equations on polarizable carnot group. Appl. Math.- J. Chin. Univ. 21, 157–164 (2006). https://doi.org/10.1007/BF02791353
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DOI: https://doi.org/10.1007/BF02791353