Rellich-Kondrakov Embedding of the Laplacian Resolvent on the Torus

Louis Omenyi

 DOI : https://dx.doi.org/10.18535/rajar/v4i1.07

 ABSTRACT:

This paper proves that the domain of the Laplacian, Δ on a closed Riemannian manifold, (M,g) is compactly embedded in L2(M). Particularly, the resolvent of the Laplacian,  (Δ+1)-1 is shown to be compactly embedded on the torus.