Suppose $\lambda_1(\Omega)$ is the minimal eigenvalue of the (minus) Laplacian with zero Dirichlet condition in a domain $\Omega$. How do I prove that if I take a smaller domain $\bar\Omega$ contained in $\Omega$, then $\lambda_1(\bar\Omega)>\lambda_1(\Omega)$?
2026-03-30 20:47:25.1774903645
laplacian eigenvalues
186 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in EIGENVALUES-EIGENVECTORS
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