On a class of nonconvex functionals and applications. (Sur une classe de fonctionnelles non convexes et applications.) (French) Zbl 0738.73025

Existence theorems in finite elasticity can not rely on the convexity of the energy functional — to assume this would contradict material objectivity. In this paper there are existence and regularity results for a very special situation, namely when the domain is an annulus or a ring. The techniques used draw heavily on the method of relaxation. In the end the author gives some applications to finite elasticity.


74B20 Nonlinear elasticity
58E30 Variational principles in infinite-dimensional spaces
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74A20 Theory of constitutive functions in solid mechanics
49J40 Variational inequalities
58J32 Boundary value problems on manifolds
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