# On the solution set of the nonconvex sweeping process

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

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

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topAndrea 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 -

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