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Ellipticity loss in isotropic elasticity. (English) Zbl 0927.74007

Summary: We prove that the equilibrium displacement of an isotropic elastic solid under imposed boundary displacement converges in the strong \(H^1\) topology when the shear modulus goes to zero. As a consequence, we show that the dependence on material constants may be dropped in the classical inequality expressing the continuous dependence of elastic equilibria on the boundary displacement.

MSC:

74B05 Classical linear elasticity
35Q72 Other PDE from mechanics (MSC2000)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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