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Linearized elasticity as $$\Gamma$$-limit of finite elasticity. (English) Zbl 1009.74008
Linearized elastic energies are derived from rescaled nonlinear energies by means of $$\Gamma$$-convergence. For Dirichlet and mixed boundary value problems in a Lipschitz domain $$\Omega$$, the convergence of minimizers takes place in the weak topology of $$H^1(\Omega,\mathbb{R}^n)$$ and in the strong topology of $$W^{1,q}(\Omega,\mathbb{R}^n)$$ for $$1\leq q<2$$.

##### MSC:
 74B15 Equations linearized about a deformed state (small deformations superposed on large) 74B20 Nonlinear elasticity 74G65 Energy minimization in equilibrium problems in solid mechanics 35Q72 Other PDE from mechanics (MSC2000)
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