: This paper proves that the domain of the Laplacian, on a closed Riemannian manifold, is compactly embedded in Particularly, the resolvent of the Laplacian, is shown to be compactly embedded on the torus
: Laplacian; Resolvent; Sobolev space; Compactly embedding; Riemannian manifold; Torus. MSC class: 35P20; 35R01.
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