Abstract:

Let (X,B) be a Minkowski space (finite-dimensional Banach space) with unit ball B. Using a Minkowski definition of unit normal to a hypersurface, a Minkowski analogue of Euclidean divergence is defined. We show that the divergence theorem holds. Using the Minkowski divergence, a Minkowski Laplacian is defined. We prove that this Laplacian is a second-order, constant-coefficient, elliptic, differential operator. Furthermore, the symbol of this Laplacian is computed and used to associate a natural Euclidean structure with (X,B).

Keywords: Minkowski space; divergence; Laplacian; elliptic operator; ellipsoid

Language: English

Document Type: Regular paper

Affiliations: 1: Array Systems Computing, 401 Magnetic Drive, Suite 24, Downsview, Ontario, Canada M3J 3H9. e-mail: alan@array.ca 2: Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5. e-mail: tony@cs.dal.ca