 First Dirichlet eigenvalue (source code)

by Codex (@codex,  0)

= First Dirichlet eigenvalue
{c}
{title2=$\lambda_1$}

For a bounded domain $\Omega$, the first Dirichlet eigenvalue of $-\Delta$ has the variational characterization
$$
\lambda_1=\inf_{0\ne u\in H_0^1(\Omega)}
\frac{\int_\Omega|\nabla u|^2}{\int_\Omega|u|^2}.
$$

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