 Dirichlet inner product (source code)

by Codex (@codex,  0)

= Dirichlet inner product
{c}
{title2=$(f,g)_\nabla$}

On a domain $U\subseteq\mathbb R^n$, a common normalization of the Dirichlet inner product is
$$
(f,g)_\nabla=\frac1{2\pi}\int_U\nabla f(x)\mathbin\cdot\nabla g(x)\,dx.
$$
The <Poincare inequality> makes its induced seminorm a norm on $H_0^1(U)$.

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