Kavli Affiliate: Zheng Zhu
| First 5 Authors: Tian Liang, Zheng Zhu, , ,
| Summary:
In this article, we study local Sobolev-Poincar’e imbedding domains. The
main result reads as below. begin{enumerate} item for $1leq pleq n$, a
bounded uniform domain is also a local Sobolev-Poincar’e imbedding domain of
order $p$; conversely a local Sobolev-Poincar’e imbedding domain of order $p$
is locally linearly connected $(LLC)$. A uniform domain is $(LLC)$. Conversely,
with some very weak connecting assumption, a $(LLC)$ domain is uniform. item
for $n<p<fz$, a bounded domain is a local Sobolev-Poincar’e imbedding domain
of order $p$ if and only if it is an $alpha$-cigar domain for
$alpha=(p-n)/(p-1)$. Hence, a domain is a local Sobolev-Poincar’e imbedding
domain of oder $p$ if and only if it is a (global) Sobolev-Poincar’e imbedding
domain. end{enumerate}
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