TY - CHAP
T1 - Traces
AU - Brezis, Haïm
AU - Mironescu, Petru
N1 - Publisher Copyright:
© 2021, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021
Y1 - 2021
N2 - We present a complete trace theory for S1 -valued maps. When s> 0 is not an integer and 1 ≤ p< ∞, standard trace theory for real-valued maps asserts that trΩWs+1/p,p(Ω×(0,1);R)=Ws,p(Ω;R), where we identify Ω with Ω× { 0 }. When R is replaced by a manifold N, in general we only have the inclusion trΩWs+1/p,p(Ω×(0,1);N)⊂Ws,p(Ω;N), and equality may fail.
AB - We present a complete trace theory for S1 -valued maps. When s> 0 is not an integer and 1 ≤ p< ∞, standard trace theory for real-valued maps asserts that trΩWs+1/p,p(Ω×(0,1);R)=Ws,p(Ω;R), where we identify Ω with Ω× { 0 }. When R is replaced by a manifold N, in general we only have the inclusion trΩWs+1/p,p(Ω×(0,1);N)⊂Ws,p(Ω;N), and equality may fail.
UR - http://www.scopus.com/inward/record.url?scp=85122470538&partnerID=8YFLogxK
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U2 - 10.1007/978-1-0716-1512-6_11
DO - 10.1007/978-1-0716-1512-6_11
M3 - Chapter
AN - SCOPUS:85122470538
T3 - Progress in Nonlinear Differential Equations and Their Application
SP - 331
EP - 337
BT - Progress in Nonlinear Differential Equations and Their Application
PB - Birkhauser
ER -