Title

Self-adjointness of the Gaffney Laplacian on Vector Bundles

Document Type

Article

Publication Date

12-26-2015

Abstract

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.

Publication Title

Mathematical Physics Analysis and Geometry

Volume

18

Issue

1

Digital Object Identifier (DOI)

10.1007/s11040-015-9188-3

ISSN

13850172

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