Many nonequilibrium rate independent processes arising in elastoplasticity, ferromagnetism and phase transitions are described by an evolution variational inequality with a convex constraint in a Hilbert space. The resulting solution operator is called "play operator" and acts on absolutely continuous functions. For nonregular data two natural notions of BV solutions have been proposed by the authors, giving rise to different extensions of the play operator to BV. We prove that these extensions are equal if and only if the convex constraint is a non-obtuse polyhedron.
Comparing BV solutions of rate independent processes / Pavel Krejci; Vincenzo Recupero. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - STAMPA. - 21:1(2014), pp. 121-146.