In this paper,we analyze the asymptotic behavior of solution sequences of the Liouville-type equation with Neumann boundary condition.In particular,we will obtain a sharp mass quantization result for the solution sequ...In this paper,we analyze the asymptotic behavior of solution sequences of the Liouville-type equation with Neumann boundary condition.In particular,we will obtain a sharp mass quantization result for the solution sequences at a blow-up point.展开更多
In this paper,we investigate a singular Moser-Trudinger inequality involving L^(n) norm in the entire Euclidean space.The blow-up procedures are used for the maximizing sequence.Then we obtain the existence of extrema...In this paper,we investigate a singular Moser-Trudinger inequality involving L^(n) norm in the entire Euclidean space.The blow-up procedures are used for the maximizing sequence.Then we obtain the existence of extremal functions for this singular geometric inequality in whole space.In general,W^(1,n)(R^(n))→L^(q)(R^(n))is a continuous embedding but not compact.But in our case we can prove that W^(1,n)(R^(n))→L^(n)(R^(n))is a compact embedding.Combining the compact embedding W^(1,n)(R^(n))→Lq(R^(n),|x|^(−s)dx)for all q≥n and 0<s<n in[18],we establish the theorems for any 0≤α<1.展开更多
文摘In this paper,we analyze the asymptotic behavior of solution sequences of the Liouville-type equation with Neumann boundary condition.In particular,we will obtain a sharp mass quantization result for the solution sequences at a blow-up point.
文摘In this paper,we investigate a singular Moser-Trudinger inequality involving L^(n) norm in the entire Euclidean space.The blow-up procedures are used for the maximizing sequence.Then we obtain the existence of extremal functions for this singular geometric inequality in whole space.In general,W^(1,n)(R^(n))→L^(q)(R^(n))is a continuous embedding but not compact.But in our case we can prove that W^(1,n)(R^(n))→L^(n)(R^(n))is a compact embedding.Combining the compact embedding W^(1,n)(R^(n))→Lq(R^(n),|x|^(−s)dx)for all q≥n and 0<s<n in[18],we establish the theorems for any 0≤α<1.
