Trace Theorems for Sobolev Spaces on Lipschitz Domains. Necessary Conditions
Annales mathématiques Blaise Pascal, Volume 14 (2007) no. 2, p. 187-197

A famous theorem of E. Gagliardo gives the characterization of traces for Sobolev spaces W 1,p Ω for 1p< when Ω N is a Lipschitz domain. The extension of this result to W m,p Ω for m2 and 1<p< is now well-known when Ω is a smooth domain. The situation is more complicated for polygonal and polyhedral domains since the characterization is given only in terms of local compatibility conditions at the vertices, edges, .... Some recent papers give the characterization for general Lipschitz domains for m=2 in terms of global compatibility conditions. Here we give the necessary compatibility conditions for m3 and we prove how the local compatibility conditions can be derived.

@article{AMBP_2007__14_2_187_0,
     author = {Geymonat, Giuseppe},
     title = {Trace Theorems for Sobolev Spaces on Lipschitz Domains. Necessary Conditions},
     journal = {Annales math\'ematiques Blaise Pascal},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {14},
     number = {2},
     year = {2007},
     pages = {187-197},
     doi = {10.5802/ambp.232},
     mrnumber = {2369871},
     zbl = {1161.46019},
     language = {en},
     url = {http://www.numdam.org/item/AMBP_2007__14_2_187_0}
}
Geymonat, Giuseppe. Trace Theorems for Sobolev Spaces on Lipschitz Domains. Necessary Conditions. Annales mathématiques Blaise Pascal, Volume 14 (2007) no. 2, pp. 187-197. doi : 10.5802/ambp.232. http://www.numdam.org/item/AMBP_2007__14_2_187_0/

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