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Journal of Convex Analysis 21 (2014), No. 1, 121--146
Copyright Heldermann Verlag 2014

Comparing BV Solutions of Rate Independent Processes

Pavel Krejcí
Institute of Mathematics, Academy of Sciences, Zitná 25, 11567 Praha 1, Czech Republic

Vincenzo Recupero
Dip. di Scienze Matematiche, Politecnico di Torino, Duca degli Abruzzi 24, 10129 Torino, Italy

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.

Keywords: Variational inequalities, rate independence, convex sets.

MSC: 47J20, 74C05

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