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arXiv · 1801.09114

Rellich-Kondrakov embedding of the Laplacian resolvent on the torus

Louis Omenyi
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Abstract

This paper proves that the domain of the Laplacian, $\DEL,$ on a closed Riemannian manifold, $(M,g),$ is compactly embedded in $L^{2} (M) .$ Particularly, the resolvent of the Laplacian, $(\DEL + 1)^{-1},$ is shown to be compactly embedded on the torus.

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Louis Omenyi. 2018-01-27. Rellich-Kondrakov embedding of the Laplacian resolvent on the torus. https://doi.org/10.18535/rajar%2Fv4i1.07

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