Carnot群上的Hardy型不等式和唯一延拓性

王家林, 廖冬妮

数学学报 ›› 2015, Vol. 58 ›› Issue (4) : 577-584.

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数学学报 ›› 2015, Vol. 58 ›› Issue (4) : 577-584. DOI: 10.12386/A2015sxxb0059
论文

Carnot群上的Hardy型不等式和唯一延拓性

    王家林, 廖冬妮
作者信息 +

Hardy Type Inequality and Unique Continuation on Carnot Groups

    Jia Lin WANG, Dong Ni LIAO
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文章历史 +

摘要

给出了一般Carnot群上的Lp加权Hardy型不等式,1< p< +∞, 由此导出了Hardy—Sobolev型不等式.作为对该不等式的一个应用,考虑了一类带奇异位势的p-sub-Laplace方程,对其弱解建立了二重性和唯一延拓性.

Abstract

We show Lp weighted Hardy type inequalities for 1 < p < +∞ on general Carnot groups. Using the previous inequalities, we also obtain a Hardy-Sobolev type inequality. As an application, doubling property and unique continuation of the weak solution to p-sub-Laplacian with singular weights are established.

关键词

Hardy型不等式 / Hardy—Sobolev型不等式 / 唯一延拓性 / Carnot群

Key words

Hardy type inequality / Hardy-Sobolev type inequality / unique continuation / Carnot group

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王家林, 廖冬妮. Carnot群上的Hardy型不等式和唯一延拓性. 数学学报, 2015, 58(4): 577-584 https://doi.org/10.12386/A2015sxxb0059
Jia Lin WANG, Dong Ni LIAO. Hardy Type Inequality and Unique Continuation on Carnot Groups. Acta Mathematica Sinica, Chinese Series, 2015, 58(4): 577-584 https://doi.org/10.12386/A2015sxxb0059

参考文献

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基金

国家自然科学基金资助项目(11201081);江西省自然科学基金资助项目(20142BAB201001);赣南师范学院自然科学校级课题(13kyz10)

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