On homotopy conditions and the existence of multiple equilibria in finite elasticity
Katharina Post, Jeyabal Sivaloganathan · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1997
In this paper we study homotopy classes of deformations and their properties under weak convergence. As an application, we give an analytic proof (in two and three dimensions) of the existence of infinitely many local minimisers for a displacement boundary-value problem from finite elasticity, posed on a nonconvex domain, under the constitutive assumption of polyconvexity.