Existence result and discontinuous finite element discretization for a plane stresses Hencky problem

We hereafter propose and analyse a discontinuous finite element method for a plane stress Hencky problem. For that purpose we begin by proving an existence result for the continuous problem. A kind of Green's formula between \documentclass{article}\pagestyle{empty}\begin{document}$$ BD\left(\Omega \right) = \left\{{u \in {\rm{L}}^1 \left(\Omega \right),\varepsilon _{ij} (u) \in M_1 \left(\Omega \right)} \right\}{\rm{and}}H\left(\Omega \right) = \left\{{\sigma \in L^\infty \left(\Omega \right),div\sigma \in {\rm{L}}^2 \left(\Omega \right)} \right\} $$\end{document} and other intermediate results that may be of independent interest are presented and established separately. Then we formulate the discretized problem, give an existence result for it and prove a result of weak convergence of a subsequence of discrete solutions to a solution of the continuous problem.