WIAS Preprint No. 432, (1998)

Evolution variational inequalities and multidimensional hysteresis operators.


  • Krejčí, Pavel
    ORCID: 0000-0002-7579-6002

2010 Mathematics Subject Classification

  • 58E35 47H30 73E05


  • Variational inequality, hysteresis operators




We give an overview of the theory of multidimensional hysteresis operators defined as solution operators of rate-independent variational inequalities in a Hilbert space X with given convex constraints. Emphasis is put on analytical properties of these operators in the space of functions of bounded variation with values in X, in Sobolev spaces and in the space of continuous functions. We discuss in detail the influence of the geometry of the convex constraint on the input-output behavior. It is shown how multidimensional hysteresis operators arise naturally in constitutive laws of rate-independent plasticity and concrete examples of application of the above theory in material sciences are given.

Appeared in

  • Nonlinear Differential Equations (Drabete, P, Krejci, P., Takac, P., eds.) Boca Raton: Chapman & Hall, 1999, CRC Res. Notes Math. 404, pp. 47--110

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