The play operator on the rectifiable curves in a Hilbert space. (English) Zbl 1140.74021
Summary: The vector play operator is the solution operator of a class of evolution variational inequalities arising in continuum mechanics. For regular data, the existence of solutions is easily obtained from general results on maximal monotone operators. If the datum is a continuous function of bounded variation, then the existence of a weak solution is usually proved by means of a time discretization procedure. In this paper we give a short proof of the existence of play operator on rectifiable curves making use of basic facts of measure theory. We also drop the separability assumptions usually made by other authors.
MSC:
| 74N30 | Problems involving hysteresis in solids |
| 47H60 | Multilinear and polynomial operators |
| 26A45 | Functions of bounded variation, generalizations |
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