Kavli Affiliate: Zheng Zhu
| First 5 Authors: Tian Liang, Zheng Zhu, , ,
| Summary:
In this article, we study local Sobolev-Poincar’e imbedding domains. We
prove under some connecting assumption,
(1) for $1leq pleq n$, a domain is a local Sobolev-Poincar’e imbedding
domain of order $p$ if and only if it is a uniform domain, a local
Sobolev-Poincar’e imbedding domain of order $p$ is also a (global)
Sobolev-Poincar’e imbedding domain of order $p$, but the converse is not
always correct;
(2) for $n<p<infty$, a domain is a local Sobolev-Poincar’e imbedding domain
of order $p$ if and only if it is an $alpha$-cigar domain for
$alpha=(p-n)/(p-1)$, 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.
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