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Sobolev space

Poincare inequality

Poincare-Wirtinger inequality

{title2=$H^1_\dagger(U)$}

The mean-zero Sobolev space is the closed subspace
$$
H^1_\dagger(U)=\left\{u\in H^1(U):\int_Uu=0\right\}.
$$
On a bounded connected Lipschitz domain, the <Poincare-Wirtinger inequality> makes $\|\nabla u\|_2$ an equivalent Hilbert norm on this space.

Mean-zero Sobolev space

Paper 105 / 1 / d / Solution

Mean-zero Sobolev space ( $H_{†}^{1} (U)$ )

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Mean-zero Sobolev space (H†1​(U))

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