Abstract:
We introduce a new space of generalised functions with bound ed variation to prove the existence of a solution to a minimum problem
that arises in the variational approach to fracture mechanics in elasto plastic materials. We study the fine properties of the functions belonging
to this space and prove a compactness result. In order to use the Direct
Method of the Calculus of Variations we prove a lower semicontinuity
result for the functional occurring in this minimum problem. Moreover,
we adapt a nontrivial argument introduced by Friedrich to show that
every minimizing sequence can be modified to obtain a new minimizing
sequence that satisfies the hypotheses of our compactness result.
