Re: Image of trace (Sobolev spaces)
- From: craig <ctcowan@xxxxxxxxxxx>
- Date: Wed, 29 Aug 2007 11:13:20 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?
Heres a related question which notation suggests is correct but I have never seen it any where.
Let T be as above. Then one has
T:H^1(Omega) -> H^{1/2}(partial Omega) is continuous
where H^{1/2} is defined using some interpolation ideas which I have no clue about.
In any case notation suggests taht
H^{1/2}(partial Omega) is complactly imbedded in
L^2(\partial Omega).
Is this correct?
(If so then T:H^1(Omega)-> L^2(partial Omega) would be compact which I think is probably false)
thanks
craig
.
thanks
craig
- References:
- Image of trace (Sobolev spaces)
- From: craig
- Image of trace (Sobolev spaces)
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