Re: Traces ( H^1(\Omega) )

On Tue, 18 Apr 2006 02:16:22 GMT, Stephen Montgomery-Smith
<stephen@xxxxxxxxxxxxxxxxx> wrote:

don wrote:
Just wondering if anyone knows the answer to the following:

Take $ \Omega $ to be open, bounded and smooth domain.

Question: Is the following set dense in $L^2( \partial \Omega) $.

(( $ \partial \Omega $ is the boundary of $ \Omega$))

The set is the set of $ C^infinity( \overline(\Omega)) $ functions restricted to $ \partial \Omega $.

Can we assume that C^infty(partial Omega) is dense in L_2(partial
Omega)? If so, you can extend any C^infty function on the boundary to a
C^infty function on bar Omega by solving the Laplacian equation with
Dirichlet boundary conditions.

Or by much simpler methods, like a partition of unity...


************************

David C. Ullrich
.

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