Estimation of Sobolev-type embedding constant on domains with minimally smooth boundary using extension operator

In this paper, we propose a method for estimating the Sobolev-type embedding constant from W 1 , q ( Ω ) to L p ( Ω ) on a domain Ω ⊂ R n ( n = 2 , 3 , … ) with minimally smooth boundary (also known as a Lipschitz domain), where p ∈ ( n / ( n − 1 ) , ∞ ) and q = n p / ( n + p ) . We estimate the embedding constant by constructing an extension operator from W 1 , q ( Ω ) to W 1 , q ( R n ) and computing its operator norm. We also present some examples of estimating the embedding constant for certain domains.