论文标题
几乎不可压缩的矢量场的指定弯曲
Pointwise descriptions of nearly incompressible vector fields with bounded curl
论文作者
论文摘要
在这些几乎不可压缩的矢量字段中，$ {\ bf {v}}：{\ mathbb {r}}}^n \ to {\ mathbb {r}}^n $与$ | x | x | x | x | x | x | x | x | $增长在infination in Infinity，我们给出了$ \ operatat} cul cur { d {\ bf {v}} - d^t {\ bf {v}} $属于$ l^\ infty $。当$ n = 2 $时，我们可以进一步描述，但仍以刻度的术语描述，向量字段$ {\ bf {v}}}}：{\ mathbb {r}}}^2 \ to {\ mathbb {r}}^2 $美元
Among those nearly incompressible vector fields ${\bf{v}}:{\mathbb{R}}^n\to{\mathbb{R}}^n$ with $|x|\log|x|$ growth at infinity, we give a pointwise characterization of the ones for which $\operatorname{curl}{\bf{v}}= D{\bf{v}}-D^t{\bf{v}}$ belongs to $L^\infty$. When $n=2$ we can go further and describe, still in pointwise terms, the vector fields ${\bf{v}}:{\mathbb{R}}^2\to{\mathbb{R}}^2$ for which $|\operatorname{div}{\bf{v}}|+|\operatorname{curl}{\bf{v}}|\in L^\infty$.
