Let $\Omega$ be a region or a manifold, consider the Laplacian operator with Dirichlet condition. Let $\lambda_1>0$ be the first eigen value.
Q Why the $\lambda_1$ is simple, i.e. any two eigenfunctions of the first eigenvalue must be proportional?
2026-03-24 22:17:16.1774390636
first eigen value of Laplacian
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