Ernst, Emil Ellipticity loss in isotropic elasticity. (English) Zbl 0927.74007 J. Elasticity 51, No. 3, 203-211 (1998). 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. Cited in 2 Documents 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 Keywords:well-posed problems; strong convergence; \(H(1)\)-topology; vanishing shear modulus; dependence on material constants PDFBibTeX XMLCite \textit{E. Ernst}, J. Elasticity 51, No. 3, 203--211 (1998; Zbl 0927.74007) Full Text: DOI