Rellich-Kondrakov Embedding of the Laplacian Resolvent on the Torus

: Laplacian; Resolvent; Sobolev space; Compactly embedding; Riemannian manifold; Torus. MSC class: 35P20; 35R01.

Authors

  • Louis Omenyi Department of Mathematics/Computer Science/Statistics/Informatics, Federal University, Ndufu-Alike, Ikwo, Nigeria
January 30, 2018

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: 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