论文标题
关于Sobolev功能相对于Sobolev Norm的可不同性
On differentiability of Sobolev functions with respect to the Sobolev norm
论文作者
论文摘要
我们研究了$ W^1_p $ -Diverentibility与Sobolev函数的$ L_P $ -Differentible之间的连接。我们证明，$ W^1_p $ -Differentibility意味着$ L_P $ -Differentibility，但相反的含义无效。也讨论了近似可不同性的概念。此外，我们考虑$ w^1_p $ -Differentibily的sobolev函数$ \ cp_p $ - 几乎无处不在。
We study connections between the $W^1_p$-differentiability and the $L_p$-differentiability of Sobolev functions. We prove that, $W^1_p$-differentiability implies the $L_p$-differentiability, but the opposite implication is not valid. The notion of approximate differentiability is discussed as well. In addition, we consider the $W^1_p$-differentiability of Sobolev functions $\cp_p$-almost everywhere.
