| Title:
|
Local Lipschitz continuity of the stop operator (English) |
| Author:
|
Desch, Wolfgang |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
43 |
| Issue:
|
6 |
| Year:
|
1998 |
| Pages:
|
461-477 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
hysteresis |
| Keyword:
|
stop operator |
| Keyword:
|
differential inclusion |
| Keyword:
|
Lipschitz continuity |
| MSC:
|
34A60 |
| MSC:
|
47H30 |
| MSC:
|
47J40 |
| MSC:
|
49J40 |
| idZBL:
|
Zbl 0937.47058 |
| idMR:
|
MR1652108 |
| DOI:
|
10.1023/A:1023221405455 |
| . |
| Date available:
|
2009-09-22T17:59:24Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134399 |
| . |
| Reference:
|
[1] M. Berger and B. Gostiaux: Differential Geometry: Manifolds, Curves, and Surfaces.Graduate Texts in Mathematics 115, Springer, New York, 1988. MR 0917479 |
| Reference:
|
[2] M. Brokate and P. Krejčí: Wellposedness of kinematic hardening models in elastoplasticity.Christian-Albrechts-Universität Kiel, Berichtsreihe des Mathematischen Seminars Kiel, Bericht 96–4, Februar 1996. |
| Reference:
|
[3] M. Brokate and J. Sprekels: Hysteresis and Phase Transitions.Applied Mathematical Sciences 121, Springer, New York, 1996. MR 1411908 |
| Reference:
|
[4] W. Desch and J. Turi: The stop operator related to a convex polyhedron.Manuscript. |
| Reference:
|
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| Reference:
|
[6] M. A. Krasnosel’skii and A. V. Pokrovskii: Systems with Hysteresis.Springer, Berlin, 1989. MR 0987431 |
| Reference:
|
[7] P. Krejčí: Vector hysteresis models.Euro. J. of Applied Math. 2 (1991), 281–292. MR 1123144, 10.1017/S0956792500000541 |
| Reference:
|
[8] P. Krejčí: Hysteresis, Convexity, and Dissipation in Hyperbolic Equations.Gakkotosho, Tokyo, 1996. MR 2466538 |
| Reference:
|
[9] P. Krejčí: Evolution variational inequalities and multidimensional hysteresis operators.Manuscript. |
| Reference:
|
[10] P. Krejčíand V. Lovicar: Continuity of hysteresis operators in Sobolev spaces.Appl. Math. 35 (1990), 60–66. MR 1039411 |
| Reference:
|
[11] A. Visintin: Differential Models of Hysteresis.Springer, Berlin, 1994. Zbl 0820.35004, MR 1329094 |
| . |
