We prove some sharp Hardy inequality associated with the gradient △γ=（△x,｜x｜γ [x△y） by a direct and simple approach. Moreover, similar method is applied to ob- tain some weighted sharp Rellich inequality rela...We prove some sharp Hardy inequality associated with the gradient △γ=（△x,｜x｜γ [x△y） by a direct and simple approach. Moreover, similar method is applied to ob- tain some weighted sharp Rellich inequality related to the Grushin operator in the setting of L^p. We also get some weighted Hardy and Rellich type inequalities related to a class of Greiner type operators.展开更多
The purpose of this paper is to investigate the nonexistence of positive so lutions of the following doubly nonlinear degenerate parabolic equations:{∂u=▽k·(u^(m-1)|▽ku|^(p-2)▽ku)+(w)u^(m+p-2),u(w,0)=u0(w)≥0,...The purpose of this paper is to investigate the nonexistence of positive so lutions of the following doubly nonlinear degenerate parabolic equations:{∂u=▽k·(u^(m-1)|▽ku|^(p-2)▽ku)+(w)u^(m+p-2),u(w,0)=u0(w)≥0,u(w,t)=0,inΩ×(0,T),inΩ,on∂Ω×(0,T),where Q is a Carnot-Carathéodory metric bal in IR^(2n+1)generated by Greiner vector fields,V∈L_(loc)(Ω),k∈N,m∈R,1<p<2n+2k and m+p-2>0.The better lower bound p*for m+p is found and the nonexistence results are proved for p*≤m+p<3.展开更多
Piega的产品不仅仅有技术含量,外观也是清新明快的路线,给人一种高端和时尚的感觉。如今的产品定位显然是更高端,产品的设计也更发烧,更疯狂。在高端产品方面,Piega推出了Master Line Source系列音箱,分别有Master Line Source 1、Maste...Piega的产品不仅仅有技术含量,外观也是清新明快的路线,给人一种高端和时尚的感觉。如今的产品定位显然是更高端,产品的设计也更发烧,更疯狂。在高端产品方面,Piega推出了Master Line Source系列音箱,分别有Master Line Source 1、Master Line Source 2和Master Line Source 3三款型号。Leo Greiner和Manuel Greiner告诉我,它们不仅使用了Piega著名的同轴式电磁平面振膜高/中音单元,而且还以多只高/中音单元组成线阵式结构。展开更多
We prove some Rellich type inequalities for the sub-Laplacian on Carnot nilpotent groups. Using the same method, we obtain some analogous inequalities for the Heisenberg-Greiner operators. In most cases, the constants...We prove some Rellich type inequalities for the sub-Laplacian on Carnot nilpotent groups. Using the same method, we obtain some analogous inequalities for the Heisenberg-Greiner operators. In most cases, the constants we obtained are optimal.展开更多
基金Supported by the National Natural Science Foundation(NSF) of China (11001240)NSF of Zhejiang Province(Y6090359)
文摘We prove some sharp Hardy inequality associated with the gradient △γ=（△x,｜x｜γ [x△y） by a direct and simple approach. Moreover, similar method is applied to ob- tain some weighted sharp Rellich inequality related to the Grushin operator in the setting of L^p. We also get some weighted Hardy and Rellich type inequalities related to a class of Greiner type operators.
基金support from Nature Science Fund of China(No.11771354).
文摘The purpose of this paper is to investigate the nonexistence of positive so lutions of the following doubly nonlinear degenerate parabolic equations:{∂u=▽k·(u^(m-1)|▽ku|^(p-2)▽ku)+(w)u^(m+p-2),u(w,0)=u0(w)≥0,u(w,t)=0,inΩ×(0,T),inΩ,on∂Ω×(0,T),where Q is a Carnot-Carathéodory metric bal in IR^(2n+1)generated by Greiner vector fields,V∈L_(loc)(Ω),k∈N,m∈R,1<p<2n+2k and m+p-2>0.The better lower bound p*for m+p is found and the nonexistence results are proved for p*≤m+p<3.
文摘Piega的产品不仅仅有技术含量,外观也是清新明快的路线,给人一种高端和时尚的感觉。如今的产品定位显然是更高端,产品的设计也更发烧,更疯狂。在高端产品方面,Piega推出了Master Line Source系列音箱,分别有Master Line Source 1、Master Line Source 2和Master Line Source 3三款型号。Leo Greiner和Manuel Greiner告诉我,它们不仅使用了Piega著名的同轴式电磁平面振膜高/中音单元,而且还以多只高/中音单元组成线阵式结构。
基金Supported by National Science Foundation of China(10901126)Hubei Province Key Laboratory of Systems Science in Metallurgical Process(Y201106)+2 种基金National Science Foundation of Hubei Province(2010CDB03305)Wuhan Chenguang Process(201150431096)Open Fund of State Key Lab of Information Engineering in Surveying Mapping and Remote Sensing(11R01)
文摘We prove some Rellich type inequalities for the sub-Laplacian on Carnot nilpotent groups. Using the same method, we obtain some analogous inequalities for the Heisenberg-Greiner operators. In most cases, the constants we obtained are optimal.
