Estimation of Sobolev-type embedding constant on domains with minimally smooth boundary using extension operator
نویسندگان
چکیده
In this paper, we propose a method for estimating the Sobolev-type embedding constant fromW1,q( ) to Lp( ) on a domain ⊂Rn (n = 2, 3, . . . ) with minimally smooth boundary (also known as a Lipschitz domain), where p ∈ (n/(n – 1),∞) and q = np/(n + p). We estimate the embedding constant by constructing an extension operator fromW1,q( ) toW1,q(Rn) and computing its operator norm. We also present some examples of estimating the embedding constant for certain domains.
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تاریخ انتشار 2015