In this paper, we investigate the following elliptic problem involving the P- Laplacian where p 〉 1,0 〈 q 〈 p- 1, K R^n with K∈K^n and prove that the energy integral of the problem （P） satisfies a Brunn-Minkows...In this paper, we investigate the following elliptic problem involving the P- Laplacian where p 〉 1,0 〈 q 〈 p- 1, K R^n with K∈K^n and prove that the energy integral of the problem （P） satisfies a Brunn-Minkowski type inequality.展开更多
A q-analog, also called a q-extension or q-generalization is a mathematical expression parameterized by a quantity q that generalized a known expression and reduces to the known expression in the limit . There are q-a...A q-analog, also called a q-extension or q-generalization is a mathematical expression parameterized by a quantity q that generalized a known expression and reduces to the known expression in the limit . There are q-analogs for the fractional, binomial coefficient, derivative, Integral, Fibonacci numbers and so on. In this paper, we give several results, some of them are new and others are generalizations of the main results of [1]. As well as we give a generalization to the key lemma ([2], lemma 1.3).展开更多
In this paper, we establish a singular Trudinger-Moser inequality for the whole hyperbolic space H^n：u∈W^1,n（H^n）,^sup,fH^n｜ H^nu｜^ndμ≤1∫H^n ea｜u｜n/n-1-∑^n-2a^k｜u｜nk/n-1 k=0 k!/ρβ dμ〈∞ a/an＋β/n≤1...In this paper, we establish a singular Trudinger-Moser inequality for the whole hyperbolic space H^n：u∈W^1,n（H^n）,^sup,fH^n｜ H^nu｜^ndμ≤1∫H^n ea｜u｜n/n-1-∑^n-2a^k｜u｜nk/n-1 k=0 k!/ρβ dμ〈∞ a/an＋β/n≤1,where α 〉 0,β E [0,n）, ρ and dμ are the distance function and volume element of H^n respectively.展开更多
基金supported by Natural Science Foundation of China (10671064)Scientific Research Fund of Hunan Provincial Education Department (06C516)Excellent Youth Programm of Hunan Normal University (080640)
文摘In this paper, we investigate the following elliptic problem involving the P- Laplacian where p 〉 1,0 〈 q 〈 p- 1, K R^n with K∈K^n and prove that the energy integral of the problem （P） satisfies a Brunn-Minkowski type inequality.
文摘A q-analog, also called a q-extension or q-generalization is a mathematical expression parameterized by a quantity q that generalized a known expression and reduces to the known expression in the limit . There are q-analogs for the fractional, binomial coefficient, derivative, Integral, Fibonacci numbers and so on. In this paper, we give several results, some of them are new and others are generalizations of the main results of [1]. As well as we give a generalization to the key lemma ([2], lemma 1.3).
文摘In this paper, we establish a singular Trudinger-Moser inequality for the whole hyperbolic space H^n：u∈W^1,n（H^n）,^sup,fH^n｜ H^nu｜^ndμ≤1∫H^n ea｜u｜n/n-1-∑^n-2a^k｜u｜nk/n-1 k=0 k!/ρβ dμ〈∞ a/an＋β/n≤1,where α 〉 0,β E [0,n）, ρ and dμ are the distance function and volume element of H^n respectively.
