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Applied Nonlinear Analysis pp 117–132Cite as

Remarks on the Determinant in Nonlinear Elasticity and Fracture Mechanics

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Abstract

The role of the determinant in ensuring local invertibility of Sobolev functions in W 1,N(Ω; ℝN) is studied. Weak continuity of minors of gradients of functions in W 1,p(Ω; ℝN) for p<N is fully characterized. Properties of the determinant are addressed within the framework of functions of bounded variation, and a change of variables formula is obtained. These results are relevant in the study of equilibria, cavitation, and fracture of nonlinear elastic materials.

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Authors
  1. Irene Fonseca
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  2. Jan Malý
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Editors and Affiliations

  1. I.S.T. Technical University, Lisbon, Portugal

    Adélia Sequeira  & Juha Hans Videman  & 

  2. University of Pisa, Pisa, Italy

    Hugo Beirão da Veiga

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Fonseca, I., Malý, J. (2002). Remarks on the Determinant in Nonlinear Elasticity and Fracture Mechanics. In: Sequeira, A., da Veiga, H.B., Videman, J.H. (eds) Applied Nonlinear Analysis. Springer, Boston, MA. https://doi.org/10.1007/0-306-47096-9_9

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  • DOI: https://doi.org/10.1007/0-306-47096-9_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-46303-7

  • Online ISBN: 978-0-306-47096-7

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