Annali di Matematica Pura ed Applicata

, Volume 90, Issue 1, pp 181–189 | Cite as

Hyperelasticity and the potentialness of a nonlinear operator

  • C. O. A. Sowunmi


A quasilinear second order partial differential operator of divergence form, involving N unknown functions and independent variables is transformed into a nonlinear functional operator in a Hilbert space. The constraint of potenlialness imposed on the nonlinear operator is seen to be equivalent in the case N=3 to hyperelasticity in the differential operator of elasiticity. By imposing further conditions on the differential operator, and assuming it is polynomial in the Frechet derivative of the unknown functions it becomes possible to extend to finite hyperelasticity a result proved earlier for infinitesimal hyperelasticity.


Hilbert Space Differential Operator Unknown Function Divergence Form Functional Operator 
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Copyright information

© Nicola Zanichelli Editore 1971

Authors and Affiliations

  • C. O. A. Sowunmi
    • 1
  1. 1.Nigeria

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