Existence Results for Minima of Non-Coercive Funtionals and Applications to Unilateral Problems in Elasticity
The problem of minimizing a functional on a subset of a Hilbert space is considered in a non-coercive and non-convex framework. Sufficient conditions for the existence of minima are given, involving a suitable recession functional. Some particular functionals are detailed, notably the quadratic ones, for which the existence theorem is specialized. Applications to the bending of a partially supported plate and to the classical Signorini problem are given. A modified interpretation of the unilateral condition for the Signorini problem is also introduced, suitable in finite elasticity. The abstract existence theorem is then applied to this concrete problem, providing sufficient conditions for the existence of an equilibrium configuration for an elastic body constrained to lie inside a box with rigid contour.
KeywordsVariational Inequality Equilibrium Problem Elastic Body Equilibrium Configuration Admissible Displacement
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- Fichera, G. Boundary value problems in elasticity with unilateral constraints, Handbuch der Physik, Band VIa/2, Springer Verlag, Berlin (1972), 347–389.Google Scholar
- Baiocchi, C., Gastaldi, F. and Tomarelli, F. Some existence results on non-coercive variational inequalities. Ann. Scuola Norm. Sup. Pisa (to appear).Google Scholar
- Gastaldi, F. and Tomarelli, F. Some remarks on non-linear and noncoercive variational inequalities. Boll. Un. Mat. Ital. (to appear).Google Scholar
- Ciariet, P.G. and Necas, J. Almost everywhere injectivity, self-contact and the non-vnterpenetration in non-linear, three-dimensional elasticity. (To appear).Google Scholar
- Baiocchi, C., Buttazzo, G., Gastaldi, F. and Tomarelli, F. General existence results for unilateral problems in Continuum Mechanics. (To appear).Google Scholar