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A construction of infinitely many singular weak solutions to the equations of nonlinear elasticity

  • J. Sivaloganathan (a1) and S. J. Spector (a2)

Abstract

Radial deformations of a ball composed of a nonlinear elastic material and corresponding to cavitation have been much studied. In this paper we use rescalings to show that each such deformation can be used to construct infinitely many non-symmetric singular weak solutions of the equations of nonlinear elasticity for the same displacement boundary-value problem. Surprisingly, this property appears to have been unnoticed in the literature to date.

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A construction of infinitely many singular weak solutions to the equations of nonlinear elasticity

  • J. Sivaloganathan (a1) and S. J. Spector (a2)

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