Continuity of the non-convex play operator in the space of rectifiable curves

@article{78147,
   author = {Kopfová, Jana and Recupero, Vincenzo},
   article_number = {6},
   doi = {http://dx.doi.org/10.21136/AM.2023.0257-22},
   keywords = {evolution variational inequalities; functions of bounded variation; play operator; prox-regular set; sweeping processes},
   language = {eng},
   issn = {0862-7940},
   journal = {Applications of Mathematics},
   title = {Continuity of the non-convex play operator in the space of rectifiable curves},
   url = {https://articles.math.cas.cz/10.21136/AM.2023.0257-22},
   volume = {68},
   year = {2023}
}

TY  - JOUR
ID  - 78147
AU  - Kopfová, Jana - Recupero, Vincenzo
PY  - 2023
TI  - Continuity of the non-convex play operator in the space of rectifiable curves
JF  - Applications of Mathematics
VL  - 68
IS  - 6
SP  - 727-750
EP  - 727-750
PB  - Springer Science and Business Media Deutschland GmbH
SN  - 08627940
KW  - evolution variational inequalities
KW  - functions of bounded variation
KW  - play operator
KW  - prox-regular set
KW  - sweeping processes
UR  - https://articles.math.cas.cz/10.21136/AM.2023.0257-22
N2  - We prove that the vector play operator with a uniformly prox-regular characteristic set of constraints is continuous with respect to the BV-norm and to the BV-strict metric in the space of rectifiable curves, i.e., in the space of continuous functions of bounded variation. We do not assume any further regularity of the characteristic set. We also prove that the non-convex play operator is rate independent.
ER  - 

KOPFOVÁ, Jana and Vincenzo RECUPERO. Continuity of the non-convex play operator in the space of rectifiable curves. \textit{Applications of Mathematics}. Springer Science and Business Media Deutschland GmbH, 2023, vol.~68, No~6, p.~727-750. ISSN~0862-7940. Available from: https://dx.doi.org/10.21136/AM.2023.0257-22.