Staff profile

• Calculus of variations
• Mean field games
• Nonlinear PDEs
• Optimal mass transport

Journal Article

• Graber, P. J., & Mészáros, A. R. (2024). On some mean field games and master equations through the lens of conservation laws. Mathematische Annalen, https://doi.org/10.1007/s00208-024-02859-z
• Mészáros, A. R., & Mou, C. (2024). Mean Field Games Systems under Displacement Monotonicity. SIAM Journal on Mathematical Analysis, 56(1), 529-553. https://doi.org/10.1137/22m1534353
• Graber, P. J., & Mészáros, A. R. (2023). On monotonicity conditions for mean field games. Journal of Functional Analysis, 285(9), Article 110095. https://doi.org/10.1016/j.jfa.2023.110095
• Ambrose, D. M., & Mészáros, A. R. (2023). Well-posedness of mean field games master equations involving non-separable local Hamiltonians. Transactions of the American Mathematical Society, 376(4), 2481-2523. https://doi.org/10.1090/tran/8760
• Gangbo, W., & Mészáros, A. R. (2022). Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games. Communications on Pure and Applied Mathematics, 75(12), 2685-2801. https://doi.org/10.1002/cpa.22069
• Gangbo, W., Mészáros, A. R., Mou, C., & Zhang, J. (2022). Mean field games master equations with nonseparable Hamiltonians and displacement monotonicity. Annals of Probability, 50(6), 2178-2217. https://doi.org/10.1214/22-aop1580
• Griffin-Pickering, M., & Mészáros, A. R. (2022). A variational approach to first order kinetic Mean Field Games with local couplings. Communications in Partial Differential Equations, 47(10), 1945-2022. https://doi.org/10.1080/03605302.2022.2101003
• Kwon, D., & Mészáros, A. R. (2021). Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients. Journal of the London Mathematical Society, 104(2), 688-746. https://doi.org/10.1112/jlms.12444
• Jacobs, M., Kim, I., & Mészáros, A. R. (2020). Weak Solutions to the Muskat Problem with Surface Tension Via Optimal Transport. Archive for Rational Mechanics and Analysis, 239(1), 389-430. https://doi.org/10.1007/s00205-020-01579-3
• Graber, P. J., Mészáros, A. R., Silva, F. J., & Tonon, D. (2019). The planning problem in mean field games as regularized mass transport. Calculus of Variations and Partial Differential Equations, 58(3), Article 115. https://doi.org/10.1007/s00526-019-1561-9
• Jameson Graber, P., & Mészáros, A. R. (2018). Sobolev regularity for first order mean field games. Annales de l'Institut Henri Poincaré C, 35(6), 1557-1576. https://doi.org/10.1016/j.anihpc.2018.01.002
• Kim, I., & Mészáros, A. R. (2018). On nonlinear cross-diffusion systems: an optimal transport approach. Calculus of Variations and Partial Differential Equations, 57(3), Article 79. https://doi.org/10.1007/s00526-018-1351-9
• Mészáros, A. R., & Silva, F. J. (2018). On the Variational Formulation of Some Stationary Second-Order Mean Field Games Systems. SIAM Journal on Mathematical Analysis, 50(1), 1255-1277. https://doi.org/10.1137/17m1125960
• Di Marino, S., & Mészáros, A. R. (2016). Uniqueness issues for evolution equations with density constraints. Mathematical Models and Methods in Applied Sciences, 26(09), 1761-1783. https://doi.org/10.1142/s0218202516500445
• De Philippis, G., Mészáros, A. R., Santambrogio, F., & Velichkov, B. (2016). BV Estimates in Optimal Transportation and Applications. Archive for Rational Mechanics and Analysis, 219(2), 829-860. https://doi.org/10.1007/s00205-015-0909-3
• Cardaliaguet, P., Mészáros, A. R., & Santambrogio, F. (2016). First Order Mean Field Games with Density Constraints: Pressure Equals Price. SIAM Journal on Control and Optimization, 54(5), 2672-2709. https://doi.org/10.1137/15m1029849
• Mészáros, A. R., & Santambrogio, F. (2016). Advection-diffusion equations with density constraints. Analysis & PDE, 9(3), 615-644. https://doi.org/10.2140/apde.2016.9.615
• Mészáros, A. R., & Silva, F. J. (2015). A variational approach to second order mean field games with density constraints: The stationary case. Journal de Mathématiques Pures et Appliquées, 104(6), 1135-1159. https://doi.org/10.1016/j.matpur.2015.07.008