The hydraulic elastic bulging roll system is a new roll system being developed in recent years.It is the first time in home that dead load test and study on this system has been made.Based on the experiment,the analys...The hydraulic elastic bulging roll system is a new roll system being developed in recent years.It is the first time in home that dead load test and study on this system has been made.Based on the experiment,the analysis solution of the bulging convexity of the hydraulic elastic bulging roll was obtained by selecting appropriate displacement function and adopting inverse solution of the elasticity theory.In evaluating,a variable displacement function and its solving method was advanced.The analysis results are in accord with the experiment's.Some conclusions have laid the foundation of establishing close-loop controlled mathematical model of the hydraulic elastic bulging roll system.展开更多
We consider the singular Dirichlet problem for the Monge-Ampère type equation■=0,whereΩis a strictly convex and bounded smooth domain in■is positive and strictly decreasing in(0,∞)with■is positive inΩ.We ob...We consider the singular Dirichlet problem for the Monge-Ampère type equation■=0,whereΩis a strictly convex and bounded smooth domain in■is positive and strictly decreasing in(0,∞)with■is positive inΩ.We obtain the existence,nonexistence and global asymptotic behavior of the convex solution to such a problem for more general b and g.Our approach is based on the Karamata regular variation theory and the construction of suitable sub-and super-solutions.展开更多
In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the...In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the weighted gradient estimate and uniform C^(0)estimate for the positive convex even solutions,which is a generalization of Guan-Xia[1]and Guan[2].展开更多
This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge–Ampère equation det D^2u(x) = b(x)f(u(x)), u >0, x∈Ω, where Ω is a strictly convex and bounded smooth doma...This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge–Ampère equation det D^2u(x) = b(x)f(u(x)), u >0, x∈Ω, where Ω is a strictly convex and bounded smooth domain in R^N with N ≥ 2, f is normalized regularly varying at infinity with the critical index N and has a lower term, and b∈C~∞(Ω) is positive in Ω, but may be appropriate singular on the boundary.展开更多
文摘The hydraulic elastic bulging roll system is a new roll system being developed in recent years.It is the first time in home that dead load test and study on this system has been made.Based on the experiment,the analysis solution of the bulging convexity of the hydraulic elastic bulging roll was obtained by selecting appropriate displacement function and adopting inverse solution of the elasticity theory.In evaluating,a variable displacement function and its solving method was advanced.The analysis results are in accord with the experiment's.Some conclusions have laid the foundation of establishing close-loop controlled mathematical model of the hydraulic elastic bulging roll system.
基金supported by Shandong Provincial NSF(ZR2022MA020).
文摘We consider the singular Dirichlet problem for the Monge-Ampère type equation■=0,whereΩis a strictly convex and bounded smooth domain in■is positive and strictly decreasing in(0,∞)with■is positive inΩ.We obtain the existence,nonexistence and global asymptotic behavior of the convex solution to such a problem for more general b and g.Our approach is based on the Karamata regular variation theory and the construction of suitable sub-and super-solutions.
基金Supported by National Natural Science Foundation of China(12171260).
文摘In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the weighted gradient estimate and uniform C^(0)estimate for the positive convex even solutions,which is a generalization of Guan-Xia[1]and Guan[2].
基金supported by NSF of P.R.China(Grant No.11571295)
文摘This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge–Ampère equation det D^2u(x) = b(x)f(u(x)), u >0, x∈Ω, where Ω is a strictly convex and bounded smooth domain in R^N with N ≥ 2, f is normalized regularly varying at infinity with the critical index N and has a lower term, and b∈C~∞(Ω) is positive in Ω, but may be appropriate singular on the boundary.
