p-Ginzburg-Landau型极小元的渐近性质与p-调和映射的关系

本文考虑的是一类p-Ginzburg-Landau型泛函极小元,当p∈(1,n)时的极限行为．研究了极小元的零点与p-调和映射的奇点间的关系,并证明了极小元在Cloc1,γ意义下收敛到p-调和映射．     

一类p-Ginzburg-Landau型方程解的整体收敛性

作者研究了一类p-Ginzburg-Landau型方程解的整体收敛性.通过建立正则化方程解的梯度的一致估计,最终证明了解在C^α意义下收敛.     

高维空间中一类Ginzburg-Landau型泛函的极小元的渐近分析

在空间H1,pg(Ω,Rn)中讨论如下一类变系数Ginzburg-Landau型泛函Eε(Ω)=∫Ωa(x)p|Δu|p+14εpb(x)(|u|2-β2(x))2dx的极小元列的渐近性质.这里2≤p0,m≤a(x),b(x),β(x)≤M,且a(x),b(x),β(x)是光滑函数.研究了当ε→0时极小元的渐近性态,证明了极小元列在H1,pg(Ω,Rn)中强收敛于某个元素,且得到了该元素所满足的微分方程边值问题.     

一类Ginzburg-Landau型泛函的径向极小元的渐近性

The behavior of radial minimizers for a Ginzburg-Landau type functional is considered. The weak convergence of minimizers in W1,n is improved to the strong convergence in W1,n. Some estimates of the rate of the convergence for the module of minimizers are presented.     

P-调和映射流的存在性与不唯一性

构造了ｐ 调和发展方程的初边值问题的一个整体弱解；证明了当初值ｕ０（ｘ）是弱ｐ 调和映射但不是弱ｐ 驻调和映射时问题弱解的不唯一性．     

到四元Grassmann流形的调和映射

利用奇异Darboux变换建立了四元Grassmann的因子分解并给出了其极小uniton数的上界估计。     

关于p-调和映照的Liouville型定理

本文主要讨论一类ｐ－调和映照的不存在性问题,从而得到相应的Ｌｉｏｕｖｉｌｌｅ型定理．     

关于 p-调和映照的Liouville 型定理

本文主要讨论一类 p-调和映照的不存在性问题, 从而得到相应的 Liouville型定理.     

关于平面调和映射的Bloch常数的估计

考虑了拟正则调和映射和开的平面调和映射的Bloch常数, 得到了较好的结果,
所得结果推广了陈怀惠等及Grigoryan的结果.     

指数型调和映射

证明了在适当条件下,指数型能量和指数型调和映射是共形不变的.我们主要研究了指数型调和的黎曼淹没和等距浸入,还研究了与黎曼等距浸入相关的高斯映射是指数型调和.     

Liouville Type Theorem About p-Harmonic Function and p-Harmonic Map with Finite L~q-Energy

This paper deals with the p-harmonic function on a complete non-compact submanifold M isometrically immersed in an(n + k)-dimensional complete Riemannian manifold M of non-negative(n-1)-th Ricci curvature. The Liouville type theorem about the p-harmonic map with finite L~q-energy from complete submanifold in a partially nonnegatively curved manifold to non-positively curved manifold is also obtained.     

Liouville Type Theorem About p-Harmonic Function and p-Harmonic Map with Finite L-Energy

This paper deals with the p-harmonic function on a complete non-compact submanifold M isometrically immersed in an (n + k)-dimensional complete Riemannian manifold (M) of non-negative (n-1)-th Ricci curvature.The Liouville type theorem about the p-harmonic map with finite Lq-energy from complete submanifold in a partially nonnegatively curved manifold to non-positively curved manifold is also obtained.     

Qualitative Properties of Maximum Distance Minimizers and Average Distance Minimizers in Rn

We consider one-dimensional networks of finite length in minimizing the average distance functional and the maximum distance functional subject to the length constraint. Under natural conditions, such minimizers use maximum available length, cannot contain closed loops (i.e., homeomorphic images of a circumference S¹), and have some mild regularity properties.Bibliography: 11 titles.     

A Theorem of Liouville Type for p-Harmonic Morphisms

In this article we prove a Liouville type theorem for p-harmonic morphisms. We show that if : MNis a p-harmonic morphism (p2) from a complete noncompact Riemannian manifold Mof nonnegative Ricci curvature into a Riemannian manifold Nof nonpositive scalar curvature such that the p-energy E _p (), or (2p–2)-energy E _2p–2() is finite, then is constant.     

On the Zeros and Asymptotic Behavior of Minimizers to the Ginzburg-Landau Functional with Variable Coefficient

In this paper a partial answer to the fourth open problem of Bethuel-Brezis- Hélein [1] is given. When the boundary datum has topological degree ± 1, the asymptotic behavior of minimizers of the Ginzburg-Landau functional with variable coefficient \frac{1}{x_1} is given. The singular point is located.     

Asymptotic Dirichlet Problem for Harmonic Maps with Bounded Image

Existence and uniqueness is proved for asymptotic Dirichlet problems on Hadamard manifolds. This includes manifolds of bounded negative curvature and symmetric spaces of higher rank.     

低于临界增长р-调和型方程组的完全正则性

当P≥2时,得到一类低于临界增长的退化椭圆型方程组弱解微商属于局部Morrey-Campanauo空间LP,λ和LP,r;在附加条件下,进一步建立其弱解微商的局部H(o)lder连续性.     

Equilibria of Pairs of Nonlinear Maps Associated with Cones

Let K₁, K₂ be closed, full, pointed convex cones in finite-dimensional real vector spaces of the same dimension, and let F : K₁ span K₂ be a homogeneous, continuous, K₂-convex map that satisfies F(K₁) int K₂= and FK₁ int K₂ . Using an equivalent formulation of the Borsuk-Ulam theorem in algebraic topology, we show that we have and We also prove that if, in addition, G : K₁ span K₂ is any homogeneous, continuous map which is (K₁, K₂)-positive and K₂-concave, then there exist a unique real scalar ₀ and a (up to scalar multiples) unique nonzero vector x₀ K₁ such that Gx₀ = ₀Fx₀, and moreover we have ₀ > 0 and x₀ int K₁ and we also have a characterization of the scalar ₀. Then, we reformulate the above result in the setting when K₁ is replaced by a compact convex set and recapture a classical result of Ky Fan on the equilibrium value of a finite system of convex and concave functions.