Critical mass phenomena and blow-up behaviors of ground states in stationary second order mean-field games systems with decreasing cost
Year: 2025
Type: article
Abstract: This paper is devoted to the study of Mean-field Games (MFG) systems in the mass-critical exponent case. We first derive 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 M < M ⁎ . Moreover, the blow-up behavior of energy minimizers is characterized as M ↗ M ⁎ . In particular, by considering the precise asymptotic expansions of the potential, we establish the refined blow-up behavior of ground states as M ↗ M ⁎ . While studying the existence of least-energy solutions, we establish new local W 2 , p estimates for solutions to Hamilton-Jacobi equations with superlinear gradient terms.
Authors: Marco Cirant, Fanze Kong, Juncheng Wei, Xiaoyu Zeng
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,900
OpenAlex ID: W4407945946