海森堡群上Kohn-Laplace方程的Orlicz最优正则性 |
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引用本文: | 郭欠霞. 海森堡群上Kohn-Laplace方程的Orlicz最优正则性[J]. 纺织高校基础科学学报, 2017, 0(4): 516-521. DOI: 10.13338/j.issn.1006-8341.2017.04.012 |
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作者姓名: | 郭欠霞 |
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基金项目: | 国家自然科学基金资助项目,山西省自然科学基金资助项目,山西省高等学校科技创新基金资助项目 |
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摘 要: | 通过估计海森堡群上Kohn-Laplace算子在原点的基本解的二阶导数,证明了海森堡群上Kohn-Laplace方程的Orlicz正则性估计中的增长性条件Δ_2∩▽_2是最优的,从而将欧氏空间中Poisson方程的Orlicz最优正则性结果推广到海森堡群上.
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Optimal Orlicz regularity for Kohn-Laplace equation in the Heisenberg group |
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Abstract: | By estimating the second order derivatives of the fundamental solution of Kohn-La-place operator in the Heisenberg group at the origin ,it is proved that the grow th condition Δ2∩ ▽ 2 in the Orlicz regularity estimates for the Kohn-Laplace equation in the Heisenberg group is optimal .The optimal Orlicz regularity of Poisson equation in Euclidean space is extended to the Heisenberg group . |
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