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Sturm-Liouville theory

Sturm-Liouville problem

Dirichlet eigenvalue

{c}
{title2=$\lambda_1$}

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


First Dirichlet eigenvalue

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 107 / 4 / b / iii / Solution

First Dirichlet eigenvalue ( $λ_{1}$ )

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First Dirichlet eigenvalue (λ1​)

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