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Théorèmes d’existence en calcul des variations et applications à l’élasticité nonlinéaire. (Existence theorems in the calculus of variations and applications to nonlinear elasticity.). (French) Zbl 0681.49004

Summary: We study problems of the form: \[ Inf\{\int_{\Omega}g(| \nabla v|)dx+\int_{\Omega}f(x,v)dx\}. \] We obtain some existence and regularity results when \(\Omega\) is either a ball or an annulus, without convexity hypothesis on g. We then apply these results to some shear problems in nonlinear elasticity.

MSC:

49J10 Existence theories for free problems in two or more independent variables
74S30 Other numerical methods in solid mechanics (MSC2010)
49J45 Methods involving semicontinuity and convergence; relaxation
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