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Hysteresis filtering in the space of bounded measurable functions. (English) Zbl 1177.35125
Summary: We define a mapping which with each function $$u \in L^{\infty} (0,T)$$ and an admissible value of $$r>0$$ associated the function $$\xi$$ with a prescribed initial condition $$\xi^0$$ which minimizes the total variation in the $$r$$-neighborhood of $$u$$ in each subinterval $$[0,t]$$ of $$[0,T]$$. We show that this mapping is non-expansive with respect to $$u,r$$ and $$\xi^0$$, and coincides with the so-called play operator if $$u$$ is a regulated function.

##### MSC:
 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 74N30 Problems involving hysteresis in solids
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