# Local Lipschitz continuity of the stop operator

Applications of Mathematics (1998)

- Volume: 43, Issue: 6, page 461-477
- ISSN: 0862-7940

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topDesch, Wolfgang. "Local Lipschitz continuity of the stop operator." Applications of Mathematics 43.6 (1998): 461-477. <http://eudml.org/doc/33021>.

@article{Desch1998,

abstract = {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.},

author = {Desch, Wolfgang},

journal = {Applications of Mathematics},

keywords = {hysteresis; stop operator; differential inclusion; Lipschitz continuity; hysteresis; stop operator; differential inclusions; Lipschitz continuity},

language = {eng},

number = {6},

pages = {461-477},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Local Lipschitz continuity of the stop operator},

url = {http://eudml.org/doc/33021},

volume = {43},

year = {1998},

}

TY - JOUR

AU - Desch, Wolfgang

TI - Local Lipschitz continuity of the stop operator

JO - Applications of Mathematics

PY - 1998

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 43

IS - 6

SP - 461

EP - 477

AB - 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.

LA - eng

KW - hysteresis; stop operator; differential inclusion; Lipschitz continuity; hysteresis; stop operator; differential inclusions; Lipschitz continuity

UR - http://eudml.org/doc/33021

ER -

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