| Autor: |
Cirant, Marco, Kong, Fanze, Wei, Juncheng, Zeng, Xiaoyu |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
This paper is devoted to the study of Mean-field Games (MFG) systems in the mass critical exponent case. We firstly establish the optimal Gagliardo-Nirenberg type inequality associated with the potential-free MFG system. Then, under some mild assumptions on the potential function, we show that there exists a critical mass $M^*$ such that the MFG system admits a least energy solution if and only if the total mass of population density $M$ satisfies $MComment: 58 pages; appendix was updated |
| Databáze: |
arXiv |
| Externí odkaz: |
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