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BV solutions of rate independent differential inclusions

Pavel Krejčí;  Vincenzo Recupero — 2014

Mathematica Bohemica

We consider a class of evolution differential inclusions defining the so-called stop operator arising in elastoplasticity, ferromagnetism, and phase transitions. These differential inclusions depend on a constraint which is represented by a convex set that is called the characteristic set. For BV (bounded variation) data we compare different notions of BV solutions and study how the continuity properties of the solution operators are related to the characteristic set. In the finite-dimensional case...

Continuity of the non-convex play operator in the space of rectifiable curves

Jana Kopfová;  Vincenzo Recupero — 2023

Applications of Mathematics

We prove that the vector play operator with a uniformly prox-regular characteristic set of constraints is continuous with respect to the B V -norm and to the B V -strict metric in the space of rectifiable curves, i.e., in the space of continuous functions of bounded variation. We do not assume any further regularity of the characteristic set. We also prove that the non-convex play operator is rate independent.

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