Acta Applicandae Mathematica

, Volume 71, Issue 2, pp 179–206 | Cite as

Foundations of a Nonlinear Distributional Geometry

  • Michael Kunzinger
  • Roland Steinbauer
Article

Abstract

Colombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value characterization for generalized functions on manifolds is derived, several algebraic characterizations of spaces of generalized sections are established and consistency properties with respect to linear distributional geometry are derived. An application to nonsmooth mechanics indicates the additional flexibility offered by this approach compared to the purely distributional picture.

algebras of generalized functions Colombeau algebras generalized sections of vector bundles distributional geometry 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Michael Kunzinger
    • 1
  • Roland Steinbauer
    • 1
  1. 1.Department of MathematicsUniversity of Vienna, Strudlhofg. 4, A-1090 WienAustria

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