Abstract: This is joint work with J.F. Babadjian. We investigate a functional of the gradient arising out of the theory of elasto-plasticity. It exhibits linear growth at infinity while not being a norm (so it is different from a least gradient type problem). The relaxed functional has BV minimizers. In 2d, their uniqueness may be tackled through hyperbolic methods. A mix of those with geometric measure theoretic arguments eventually leads to a uniqueness result for pure Dirichlet boundary conditions, while uniqueness is false if other types of boundary conditions are considered.

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