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Piero D'Ancona
Piero D'Ancona
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Since $Tu=T(\chi u)$ for any smooth cutoff $\chi$ equal to 1 near the boundary, the norm of the trace operator should be completely independent of the size of the open set (maybe it could be influenced by the domain being too small). For a flat boundary the norm can be computed exactly without much difficulty, then an estimate of the norm in the general case could be obtained by estimating the norm of the change of variables necessary to straighten the boundary.

Since $Tu=T(\chi u)$ for any smooth cutoff $\chi$ equal to 1 near the boundary, the norm of the trace operator should be completely independent of the size of the open set. For a flat boundary the norm can be computed exactly without much difficulty, then an estimate of the norm in the general case could be obtained by estimating the norm of the change of variables necessary to straighten the boundary.

Since $Tu=T(\chi u)$ for any smooth cutoff $\chi$ equal to 1 near the boundary, the norm of the trace operator should be independent of the size of the open set (maybe it could be influenced by the domain being too small). For a flat boundary the norm can be computed exactly without much difficulty, then an estimate of the norm in the general case could be obtained by estimating the norm of the change of variables necessary to straighten the boundary.

Source Link
Piero D'Ancona
Piero D'Ancona
  • 9k
  • 1
  • 33
  • 57

Since $Tu=T(\chi u)$ for any smooth cutoff $\chi$ equal to 1 near the boundary, the norm of the trace operator should be completely independent of the size of the open set. For a flat boundary the norm can be computed exactly without much difficulty, then an estimate of the norm in the general case could be obtained by estimating the norm of the change of variables necessary to straighten the boundary.