Image of trace (Sobolev spaces)

From: craig <ctcowan@xxxxxxxxxxx>
Date: Wed, 29 Aug 2007 10:45:43 EDT

Suppose Omega is open, bounded and smooth. Let T denote the usual trace operator.
ie. for u in H^1(Omega), Tu is the restriction of u to boundary of Omega ( \partial Omega).

Question:

Is T(H^1(Omega)) dense in L^2(partial Omega) ?

Also what classes of functions defined on partial Omega are dense in say L^2(partial Omega)?

To do this properly do I need to know some diff. geom?

thanks

craig
.

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