关于Orlicz-Sobolev类中的$p$ -模估计
On $p$-modulus estimates in Orlicz-Sobolev classes
摘要：
在$φ$上的Calderon型的条件下，我们证明了$φ$中的有限变形同胚$f$，特别是${\Bbb R}^n$中的$q>n-1$的$f\in W^{1,q}_{\rm loc}$，$n\ge 3$，是关于$p$ -模的较低的$Q$ -同胚，其中$\left[ K_{I,α}(x,f)\right]^β$，$p>n-1$和环$Q_{*}$ -关于具有$Q_{*}(x)=K_{I,α}(x,f)$的$\frac{p}{p-n+1}$ -模的同胚，其中$ K_{I,α}(x,f)$是其内部$α$ -扩张和$α=\frac{p}{p-n+1}$，$β=\frac{p-n+1}{n-1}$。
英文摘要：
Under a condition of the Calderon type on $φ$, we show that a homeomorphism $f$ of finite distortion in $W^{1,φ}_{\rm loc}$ and, in particular, $f\in W^{1,q}_{\rm loc}$ for $q>n-1$ in ${\Bbb R}^n$, $n\ge 3$, is a lower $Q$-homeomorphisms with respect to the $p$-modulus with $\left[ K_{I,α}(x,f)\right]^β$, $p>n-1$ and a ring $Q_{*}$-homeomorphism with respect to the $\frac{p}{p-n+1}$-modulus with $Q_{*}(x)=K_{I,α}(x,f)$ where $ K_{I,α}(x,f)$ is its inner $α$-dilatation and $α=\frac{p}{p-n+1}$, $β=\frac{p-n+1}{n-1}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
