Geodesic
A remark on the local Lipschitz continuity of vector hysteresis operators
Applications of Mathematics, Tome 46 (2001) no. 1, pp. 1-11 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

It is known that the vector stop operator with a convex closed characteristic $Z$ of class $C^1$ is locally Lipschitz continuous in the space of absolutely continuous functions if the unit outward normal mapping $n$ is Lipschitz continuous on the boundary $\partial Z$ of $Z$. We prove that in the regular case, this condition is also necessary.
It is known that the vector stop operator with a convex closed characteristic $Z$ of class $C^1$ is locally Lipschitz continuous in the space of absolutely continuous functions if the unit outward normal mapping $n$ is Lipschitz continuous on the boundary $\partial Z$ of $Z$. We prove that in the regular case, this condition is also necessary.
DOI : 10.1023/A:1013733403484
Classification : 34C55, 47J40, 49N60, 58E35, 74C05, 78A25
Keywords: variational inequality; hysteresis operators 
@article{10_1023_A:1013733403484,
     author = {Krej\v{c}{\'\i}, Pavel},
     title = {A remark on the local {Lipschitz} continuity of vector hysteresis operators},
     journal = {Applications of Mathematics},
     pages = {1--11},
     year = {2001},
     volume = {46},
     number = {1},
     doi = {10.1023/A:1013733403484},
     mrnumber = {1808426},
     zbl = {1067.34503},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1023/A:1013733403484/}
}
TY  - JOUR
AU  - Krejčí, Pavel
TI  - A remark on the local Lipschitz continuity of vector hysteresis operators
JO  - Applications of Mathematics
PY  - 2001
SP  - 1
EP  - 11
VL  - 46
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1023/A:1013733403484/
DO  - 10.1023/A:1013733403484
LA  - en
ID  - 10_1023_A:1013733403484
ER  - 
%0 Journal Article
%A Krejčí, Pavel
%T A remark on the local Lipschitz continuity of vector hysteresis operators
%J Applications of Mathematics
%D 2001
%P 1-11
%V 46
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1023/A:1013733403484/
%R 10.1023/A:1013733403484
%G en
%F 10_1023_A:1013733403484
Krejčí, Pavel. A remark on the local Lipschitz continuity of vector hysteresis operators. Applications of Mathematics, Tome 46 (2001) no. 1, pp. 1-11. doi: 10.1023/A:1013733403484

Cité par Sources :