Weak-strong uniqueness for solutions to mean-field games
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929734368100352 |
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| author | Ferreira, Rita Gomes, Diogo Voskanyan, Vardan |
| author_facet | Ferreira, Rita Gomes, Diogo Voskanyan, Vardan |
| contents | This paper addresses the crucial question of solution uniqueness in stationary first-order Mean-Field Games (MFGs). Despite well-established existence results, establishing uniqueness, particularly for weaker solutions in the sense of monotone operators, remains an open challenge. Building upon the framework of monotonicity methods, we introduce a linearization method that enables us to prove a weak-strong uniqueness result for stationary MFG systems on the d-dimensional torus. In particular, we give explicit conditions under which this uniqueness holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20081 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak-strong uniqueness for solutions to mean-field games Ferreira, Rita Gomes, Diogo Voskanyan, Vardan Analysis of PDEs 35J46, 35A02, 91A13, 49N90 This paper addresses the crucial question of solution uniqueness in stationary first-order Mean-Field Games (MFGs). Despite well-established existence results, establishing uniqueness, particularly for weaker solutions in the sense of monotone operators, remains an open challenge. Building upon the framework of monotonicity methods, we introduce a linearization method that enables us to prove a weak-strong uniqueness result for stationary MFG systems on the d-dimensional torus. In particular, we give explicit conditions under which this uniqueness holds. |
| title | Weak-strong uniqueness for solutions to mean-field games |
| topic | Analysis of PDEs 35J46, 35A02, 91A13, 49N90 |
| url | https://arxiv.org/abs/2502.20081 |