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The divergence theorem and the Laplacian in Minkowski space (1996)

Thompson, Alan A. ; Thompson, A. C.

Springer

Geometriae dedicata 63 (1996), S. 159-170

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ISSN: 1572-9168

Keywords: 52A21 ; Minkowski space ; divergence ; Laplacian ; elliptic operator ; ellipsoid

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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).

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00148216

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