| 可极化Carnot群上一类非散度型方程的非平凡解 |
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| 引用本文： | 刘海峰,钮鹏程.可极化Carnot群上一类非散度型方程的非平凡解[J].高校应用数学学报(英文版),2006,21(2):157-164. |
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| 作者姓名： | 刘海峰 钮鹏程 |
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| 作者单位： | Dept. Of Appl. Math. ,Northwestern Polytechnical Univ. ,Xi＇an 710072,China |
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| 基金项目： | 国家高技术研究发展计划(863计划) |
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| 摘 要： | §1Introduction WebeginbyquotingsomepreliminaryfactsontheCarnotgroupandreferthein estedreaderto1-3]formorepreciseinformationonthissubject.ALiegroupG=(Rn,o)isaCarnotgroupifthefollowingproperties(G1)(G2)hold.(G1)RncanbesplitintorsubspacesRn=Rn1×...×Rnrandthedilations(δλdefinedbyδλ(x)=(λx(1),λ2x(2),...,λrx(r)),x(j)∈Rnj areautomorphismsofG.(G2)TheLiealgebragofGisgeneratedbytheleftinvariantvectorfieldsX1,.Xn1satisfying Xj(0)=xj,j=1,...,n1.Thenaturalnumbersrand Q=n1+2n2+...+rnr…
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| 关 键 词： | 可极化 Carnot群 非散度型方程 非平凡解 |
| 收稿时间： | 2005-09-06 |
Nontrivial solutions for a class of non-divergence equations on polarizable carnot group |
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| Liu Haifeng,Niu Pencheng.Nontrivial solutions for a class of non-divergence equations on polarizable carnot group[J].Applied Mathematics A Journal of Chinese Universities,2006,21(2):157-164. |
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| Authors: | Liu Haifeng Niu Pencheng |
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| Institution: | (1) Dept. of Appl. Math., Northwestern Polytechnical Univ., 710072 Xi'an, China |
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| 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 nonhomogeneous Dirichlet problem is proved and the best possible of LQ norm in the famous Alexandrov-Bakelman-Pucci type estimate is discussed. |
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| Keywords: | Dirichlet problem polarizable Carnot group Alexandrov-Bakelman-Pucci estimate |
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