TY - JOUR
T1 - Estimation of Sobolev-type embedding constant on domains with minimally smooth boundary using extension operator
AU - Tanaka, Kazuaki
AU - Sekine, Kouta
AU - Mizuguchi, Makoto
AU - Oishi, Shin’ichi
N1 - Publisher Copyright:
© 2015, Tanaka et al.
PY - 2015/12/1
Y1 - 2015/12/1
N2 - In this paper, we propose a method for estimating the Sobolev-type embedding constant from W 1,q(Ω)to Lp(Ω) on a domain Ω⊂Rn(n=2,3…) with minimally smooth boundary (also known as a Lipschitz domain), where p∈(n/(n−1),∞)q=np/(n+p). We estimate the embedding constant by constructing an extension operator from W1,q(Ω) to W1,q(Rn) and computing its operator norm. We also present some examples of estimating the embedding constant for certain domains.
AB - In this paper, we propose a method for estimating the Sobolev-type embedding constant from W 1,q(Ω)to Lp(Ω) on a domain Ω⊂Rn(n=2,3…) with minimally smooth boundary (also known as a Lipschitz domain), where p∈(n/(n−1),∞)q=np/(n+p). We estimate the embedding constant by constructing an extension operator from W1,q(Ω) to W1,q(Rn) and computing its operator norm. We also present some examples of estimating the embedding constant for certain domains.
KW - Sobolev inequality
KW - embedding constant
KW - extension operator
UR - http://www.scopus.com/inward/record.url?scp=84949548203&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84949548203&partnerID=8YFLogxK
U2 - 10.1186/s13660-015-0907-x
DO - 10.1186/s13660-015-0907-x
M3 - Article
AN - SCOPUS:84949548203
SN - 1025-5834
VL - 2015
SP - 1
EP - 23
JO - Journal of Inequalities and Applications
JF - Journal of Inequalities and Applications
IS - 1
M1 - 389
ER -