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Self-adjointness of the Gaffney Laplacian on Vector Bundles

Lashi Bandara (Institutionen för matematiska vetenskaper, matematik) ; O. Milatovic
Mathematical Physics Analysis and Geometry (1385-0172). Vol. 18 (2015), 1, p. artikel nr 17.
[Artikel, refereegranskad vetenskaplig]

We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator.

Nyckelord: Bochner Laplacian , Essential self-adjointness , Gaffney Laplacian , Geodesically incomplete manifold , Negligible boundary , Polar boundary , Sobolev space

Denna post skapades 2015-07-20. Senast ändrad 2016-10-28.
CPL Pubid: 219852


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