# American Institute of Mathematical Sciences

June  2015, 35(6): 2405-2421. doi: 10.3934/dcds.2015.35.2405

## Weak differentiability of scalar hysteresis operators

 1 Fakultät für Mathematik, TU München, Boltzmannstr. 3, D 85747 Garching bei München 2 Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-11567 Praha 1

Received  January 2014 Revised  May 2014 Published  December 2014

Rate independent evolutions can be formulated as operators, called hysteresis operators, between suitable function spaces. In this paper, we present some results concerning the existence and the form of directional derivatives and of Hadamard derivatives of such operators in the scalar case, that is, when the driving (input) function is a scalar function.
Citation: Martin Brokate, Pavel Krejčí. Weak differentiability of scalar hysteresis operators. Discrete & Continuous Dynamical Systems - A, 2015, 35 (6) : 2405-2421. doi: 10.3934/dcds.2015.35.2405
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