A Sobolev trace on a collar extends if and only if its restriction to every member of some finite open covering extends, with a controlled energy bound.
Abbondandolo,On the homotopy type of VMO, Topol
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On the local character of the extension of traces for Sobolev mappings
A Sobolev trace on a collar extends if and only if its restriction to every member of some finite open covering extends, with a controlled energy bound.