Rellich-Kondrakov Embedding of the Laplacian Resolvent on the Torus

DATE PUBLISHED
January 30, 2018
SECTION
Articles

Abstract

: 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

 

Keywords

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

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Author Details

Louis Omenyi

  • Department of Mathematics/Computer Science/Statistics/Informatics, Federal University, Ndufu-Alike, Ikwo, Nigeria
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