An integral representation result is obtained for the relaxation of a class of energy functionals depending on two vector fields u in BV and v in Lp with 1<p≤+∞. This energy have been introduced to deal with equilibria for systems depending on chemical composition and elastic strain. In this work we add the dependence on the spatial variable x and the deformation u to the functional. Also the quasiconvexity assumption is dropped. This result may also find applications in the framework of image decomposition models. This is a joint work with Elvira Zappale.
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