I was wondering if we can compare the eigenfunctions of the Laplacian for increasing domains. In particular, I want to look at the eigenfunction for the principal eigenvalue with integral $1$. Is it possible that we could get pointwise boundedness? I have seen that the eigenvalues themselves decrease as the domains increase.
2026-04-13 02:43:13.1776048193
Eigenfunctions for Laplacian on increasing domains
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