= Dirichlet energy space
{c}
{title2=$H_0^1(D)$}
= Homogeneous Dirichlet space
{synonym}
For planar <Gaussian free field> theory, this is the completion of real <test functions> $C_c^\infty(D)$ in the norm induced by the <Dirichlet inner product>, $(f,g)_\nabla=(2\pi)^{-1}\int_D\nabla f\cdot\nabla g$. On a general unbounded domain this convention must be distinguished from completion in the inhomogeneous $H^1$ norm. A <conformal map> identifies its energy norm with that on the unit disc by conformal invariance.
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