/sci/ - Science & Math

>>14651544
How on earth did compactly supported eigenfunctions of the Laplacian work again?
IIRC [math]u \in \mathbb{ H } ^1 _0 ( \Omega )[/math] needs to zero on some compact subset of [math]\Omega[/math], which implies it's zero on an open subset of any connected component of [math]\Omega[/math], which implies it's analytic by elliptic regularity (see https://en.wikipedia.org/wiki/Elliptic_operator)), so it's zero everywhere.
What's my mistake?