Geodesic
Local Lipschitz continuity of the stop operator
Applications of Mathematics, Tome 43 (1998) no. 6, pp. 461-477.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

On a closed convex set $Z$ in ${\mathbb{R}}^N$ with sufficiently smooth (${\mathcal W}^{2,\infty }$) boundary, the stop operator is locally Lipschitz continuous from ${\mathbf W}^{1,1}([0,T],{\mathbb{R}}^N) \times Z$ into ${\mathbf W}^{1,1}([0,T],{\mathbb{R}}^N)$. The smoothness of the boundary is essential: A counterexample shows that ${\mathcal C}^1$-smoothness is not sufficient.
DOI : 10.1023/A:1023221405455
Classification : 34A60, 47H30, 47J40, 49J40
Keywords: hysteresis; stop operator; differential inclusion; Lipschitz continuity 
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     title = {Local {Lipschitz} continuity of the stop operator},
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Desch, Wolfgang. Local Lipschitz continuity of the stop operator. Applications of Mathematics, Tome 43 (1998) no. 6, pp. 461-477. doi : 10.1023/A:1023221405455. http://geodesic.mathdoc.fr/articles/10.1023/A:1023221405455/

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