On the solution set of the nonconvex sweeping process

Andrea Gavioli

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1999)

  • Volume: 19, Issue: 1-2, page 45-65
  • ISSN: 1509-9407

Abstract

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We prove that the solutions of a sweeping process make up an R δ -set under the following assumptions: the moving set C(t) has a lipschitzian retraction and, in the neighbourhood of each point x of its boundary, it can be seen as the epigraph of a lipschitzian function, in such a way that the diameter of the neighbourhood and the related Lipschitz constant do not depend on x and t. An application to the existence of periodic solutions is given.

How to cite

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Andrea Gavioli. "On the solution set of the nonconvex sweeping process." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 19.1-2 (1999): 45-65. <http://eudml.org/doc/275880>.

@article{AndreaGavioli1999,
abstract = {We prove that the solutions of a sweeping process make up an $R_δ$-set under the following assumptions: the moving set C(t) has a lipschitzian retraction and, in the neighbourhood of each point x of its boundary, it can be seen as the epigraph of a lipschitzian function, in such a way that the diameter of the neighbourhood and the related Lipschitz constant do not depend on x and t. An application to the existence of periodic solutions is given.},
author = {Andrea Gavioli},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {nonconvex; sweeping process; wedged; solution set; topological structure; periodic solutions},
language = {eng},
number = {1-2},
pages = {45-65},
title = {On the solution set of the nonconvex sweeping process},
url = {http://eudml.org/doc/275880},
volume = {19},
year = {1999},
}

TY - JOUR
AU - Andrea Gavioli
TI - On the solution set of the nonconvex sweeping process
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1999
VL - 19
IS - 1-2
SP - 45
EP - 65
AB - We prove that the solutions of a sweeping process make up an $R_δ$-set under the following assumptions: the moving set C(t) has a lipschitzian retraction and, in the neighbourhood of each point x of its boundary, it can be seen as the epigraph of a lipschitzian function, in such a way that the diameter of the neighbourhood and the related Lipschitz constant do not depend on x and t. An application to the existence of periodic solutions is given.
LA - eng
KW - nonconvex; sweeping process; wedged; solution set; topological structure; periodic solutions
UR - http://eudml.org/doc/275880
ER -

References

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