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arXiv · 2203.07534

Elliptic operators on non-compact manifolds have closed range

Luther Rinehart
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Abstract

We show that a second-order elliptic differential operator $P$, on any manifold $M$, has closed range in $C^\infty(M)$. If $M$ has no compact components, then $P$ is surjective on $C^\infty(M)$. Applications to Helmholtz decomposition are discussed.

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Luther Rinehart. 2022-03-14. Elliptic operators on non-compact manifolds have closed range. https://arxiv.org/abs/2203.07534

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