Limit Load

Many problems arising in the theory of plasticity and geometry involve Lagrangians of the form |ξ|, $$\sqrt {1 + {{\left| \xi \right|}^2}}$$. The associated functionals are defined on the Sobolev space W1(Q) which is not reflexive, and therefore the variational problem may happen to possess no solution. For this reason it is natural to find a wider space containing W1(Q) and to extend the integral functional to that space, so that the minimum could be attained on the new space. This problem has been the subject of intensive research in the theory of plasticity.