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 
@article{10_1023_A_1023221405455,
     author = {Desch, Wolfgang},
     title = {Local {Lipschitz} continuity of the stop operator},
     journal = {Applications of Mathematics},
     pages = {461--477},
     publisher = {mathdoc},
     volume = {43},
     number = {6},
     year = {1998},
     doi = {10.1023/A:1023221405455},
     mrnumber = {1652108},
     zbl = {0937.47058},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1023/A:1023221405455/}
}
TY  - JOUR
AU  - Desch, Wolfgang
TI  - Local Lipschitz continuity of the stop operator
JO  - Applications of Mathematics
PY  - 1998
SP  - 461
EP  - 477
VL  - 43
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1023/A:1023221405455/
DO  - 10.1023/A:1023221405455
LA  - en
ID  - 10_1023_A_1023221405455
ER  - 
%0 Journal Article
%A Desch, Wolfgang
%T Local Lipschitz continuity of the stop operator
%J Applications of Mathematics
%D 1998
%P 461-477
%V 43
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1023/A:1023221405455/
%R 10.1023/A:1023221405455
%G en
%F 10_1023_A_1023221405455
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

Cité par Sources :