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Nonlocal-interaction equations on uniformly prox-regular sets

Abstract:

We study the well-posedness of a class of nonlocal-interaction equations on general domains Ω⊂Rd, including nonconvex ones. We show that under mild assumptions on the regularity of domains (uniform proxregularity), for -geodesically convex interaction and external potentials, the nonlocal-interaction equations have unique weak measure solutions. Moreover, we show quantitative estimates on the stability of solutions which quantify the interplay of the geometry of the domain and the convexity o...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.3934/dcds.2016.36.1209

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
American Institute of Mathematical Sciences
Journal:
Discrete & Continuous Dynamical Systems More from this journal
Volume:
36
Issue:
3
Pages:
1209-1247
Publication date:
2016-03-01
DOI:
EISSN:
1553-5231
ISSN:
1078-0947
Language:
English
Keywords:
Pubs id:
1098268
Local pid:
pubs:1098268
Deposit date:
2020-04-17

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