Space mappings with bounded distortion
Space mappings with bounded distortion
复制标题
具有有限失真的空间映射
DOI：
10.1007/bf02196429
复制
发表时间：
1967
影响因子：
0.5
通讯作者：
Yu. G. Reshetnyak
中科院分区：
文献类型：
--
作者：
Yu. G. Reshetnyak
引言 实变函数理论中的一些事实 具有广义导数的函数 莫比乌斯变换 具有有界畸变映射的定义 黎曼空间上具有有界畸变的映射 具有有界畸变映射理论的主要事实 具有有界畸变映射的连续性模和可微性模的估计 几乎处处具有有界畸变映射的连续性和可微性模的估计 关于 $R^n$ 上连续映射的一些事实 共形容量 外部形式的广义微分的概念 具有有界畸变和椭圆微分方程 有界畸变映射的拓扑性质 有界畸变映射的局部结构 通过拟一致特性表征有界畸变映射 有界畸变映射的序列 有界畸变映射和局部同胚映射的分支点集 有界畸变映射的极值性质 一些进一步的结果 实变量函数理论和偏微分方程理论中的一些结果 有界平均振荡函数拟线性椭圆方程的哈纳克不等式 变分法泛函的半连续性和泛函收敛定理 具有广义导数的函数的一些性质 关于映射的程度。
Introduction Some facts from the theory of functions of a real variable Functions with generalized derivatives Mobius transformations Definition of a mapping with bounded distortion Mappings with bounded distortion on Riemannian spaces Main facts in the theory of mappings with boundd distortion Estimates of the moduli of continuity and differentiability almost everywhere of mappings with bounded distortion Some facts about continuous mappings on $R^n$ Conformal capacity The concept of the generalized differential of an exterior form Mappings with bounded distortion and elliptic differential equations Topological properties of mappings with bounded distortion Local structure of mappings with bounded distortion Characterization of mappings with bounded distortion by the property of quasiconformity Sequences of mappings with bounded distortion The set of branch points of a mapping with bounded distortion and locally homeomorphic mappings Extremal properties of mappings with bounded distortion Some further results Some results in the theory of functions of a real variable and the theory of partial differential equations Functions with bounded mean oscillation Harnack's inequality for quasilinear elliptic equations Theorems on semicontinuity and convergence with a functional for functionals of the calculus of variations Some properties of functions with generalized derivatives On the degree of a mapping.