Quantitative maximal L2‐regularity for viscous Hamilton–Jacobi PDEs in 2D and Mean Field Games

Abstract We discuss quantitative Calderón–Zygmund estimates in for 2D viscous Hamilton–Jacobi equations with natural growth in the gradient. We apply the result to obtain the existence of classical solutions for stationary second‐order mean field games systems in 2D with (defocusing) coupling behaving like for any . We also survey on the known results for the regularity of viscous Hamilton–Jacobi equations and second‐order Mean Field Games providing a list of several open problems.