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) no. 2, pp. 307-314
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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).
Classification :
34A47, 34B15, 34C11, 46E35
Keywords: trace theory; anisotropic Sobolev spaces
Keywords: trace theory; anisotropic Sobolev spaces
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author = {Weidemaier, Peter},
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},
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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) no. 2, pp. 307-314. http://geodesic.mathdoc.fr/item/CMUC_1991__32_2_a12/