I came across the term $W^{1,2}_0$. Just a quick question on what the 0 means and is it a Hilbert space?
I know $W^{1,2}$ is a Hilbert space.
Thanks!
2026-04-13 08:13:57.1776068037
Is $W^{1,2}_0$ a Hilbert space?
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It's the closure of $C^\infty_c(\Omega)$ with respect to $ ||.||_{1,2}$ and is thought of as the space of Sobolev functions with zero boundary value. As closure of a linear subspace in a Hilbert space it is a Hilbert space, too.
See, e.g., this Wikipedia entry