Alpár R. Mészáros, PhD Université Paris-Sud, Orsay

(email at alpar.r.meszaros@durham.ac.uk)

Research Groups

Department of Mathematical Sciences

• Applied & Computational Mathematics
• Applied & Computational Mathematics: Analysis & Partial Differential Equations

Research Interests

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

Selected Publications

Journal Article

• Jacobs, Matt, Kim, Inwon & Mészáros, Alpár R. (2021). Weak Solutions to the Muskat Problem with Surface Tension Via Optimal Transport. Archive for Rational Mechanics and Analysis 239(1): 389–430.
• Graber, P. Jameson, Mészáros, Alpár R., Silva, Francisco J. & Tonon, Daniela (2019). The planning problem in mean field games as regularized mass transport. Calculus of Variations and Partial Differential Equations 58(3): 115.
• Kim, Inwon & Mészáros, Alpár Richárd (2018). On nonlinear cross-diffusion systems: an optimal transport approach. Calculus of Variations and Partial Differential Equations 57(3): 79.
• Mészáros, Alpár Richárd & Silva, Francisco J. (2018). On the Variational Formulation of Some Stationary Second-Order Mean Field Games Systems. SIAM Journal on Mathematical Analysis 50(1): 1255-1277.
• Jameson Graber, P. & Mészáros, Alpár R. (2018). Sobolev regularity for first order mean field games. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 35(6): 1557-1576.
• Mészáros, Alpár Richárd & Santambrogio, Filippo (2016). Advection-diffusion equations with density constraints. Analysis & PDE 9(3): 615-644.
• De Philippis, Guido, Mészáros, Alpár Richárd, Santambrogio, Filippo & Velichkov, Bozhidar (2016). BV Estimates in Optimal Transportation and Applications. Archive for Rational Mechanics and Analysis 219(2): 829-860.
• Cardaliaguet, Pierre, Mészáros, Alpár R. & Santambrogio, Filippo (2016). First Order Mean Field Games with Density Constraints: Pressure Equals Price. SIAM Journal on Control and Optimization 54(5): 2672-2709.
• Di Marino, Simone & Mészáros, Alpár Richárd (2016). Uniqueness issues for evolution equations with density constraints. Mathematical Models and Methods in Applied Sciences 26(09): 1761-1783.
• Mészáros, Alpár Richárd & Silva, Francisco 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.

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