论文标题
riemannian流形之间的谐波图的能量估计
Energy estimates of harmonic maps between Riemannian manifolds
论文作者
论文摘要
令$ω\ subset {r}^n，$ $ n \ geq 3，$为有限的开放集，$ x =（x_1，x_2，x_2，\ ldots，x_n）$ a属于$ω，$ $ $ $ u \ u \ u \ u \ u \ u \ colonω\ to {r}^n，$ n> $ n> $ n> $ n> 1，d_ d_ \ partial/\ partialx_α，$ $ a = 1，\ ldots，n，\，$ $ i = 1，\ ldots，n。\，$ 主要目标是研究非不同功能的最小值的规律性$$ {\ cal f} \，= \，\int_Ωf（x，x，u，u，du）dx。 $$具有整体功能不同的平滑形状。该方法基于对功能的一些大量化，而不是与之相关的众所周知的欧拉方程。
Let $Ω\subset {R}^n,$ $n \geq 3,$ be a bounded open set, $x=(x_1,x_2,\ldots,x_n)$ a generic point which belongs to $Ω,$ $u \colon Ω\to {R}^N ,$ $N>1,$ and $ Du=(D_αu^i)$, $D_α= \partial/\partial x_α, $ $α=1,\ldots,n,\,$ $i=1,\ldots,N .\,$ Main goal is the study of regularity of the minima of nondifferentiable functionals $$ {\cal F} \,=\, \int_ΩF(x,u,Du) dx. $$ having the integrand function different shapes of smoothness. The method is based on the use some majorizations for the functional, rather than the well known Euler equation associated to it.
