The trace theorem $W^{2,1}_p(\Omega_T) \ni f \mapsto \nabla_{\!x} f \in W^{1-1/p,1/2-1/2p}_p(\partial \Omega_T)$ revisited
Weidemaier, Peter
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991), p. 307-314 / Harvested from Czech Digital Mathematics Library
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Filling a possible gap in the literature, we give a complete and readable proof of this trace theorem, which also shows that the imbedding constant is uniformly bounded for $T \downarrow 0$. The proof is based on a version of Hardy's inequality (cp. Appendix).

Publié le : 1991-01-01
Classification:  34A47,  34B15,  34C11,  46E35 
@article{116972,
     author = {Peter Weidemaier},
     title = {The trace theorem  $W^{2,1}\_p(\Omega\_T) \ni f \mapsto \nabla\_{\!x} f \in W^{1-1/p,1/2-1/2p}\_p(\partial \Omega\_T)$ revisited},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {32},
     year = {1991},
     pages = {307-314},
     zbl = {0770.46018},
     mrnumber = {1137792},
     language = {en},
     url = {http://dml.mathdoc.fr/item/116972}
}

Weidemaier, Peter. The trace theorem  $W^{2,1}_p(\Omega_T) \ni f \mapsto \nabla_{\!x} f \in W^{1-1/p,1/2-1/2p}_p(\partial \Omega_T)$ revisited. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 307-314. http://gdmltest.u-ga.fr/item/116972/

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