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Nonlinear elliptic systems and mean eld games


In this paper we consider a class of quasilinear elliptic systems of PDEs which arise in the mean eld games theory of J-M Lasry and P-L. Lions. We provide a wide range of su cient conditions for existence of solutions to these systems: on one hand the Hamiltonians ( rst-order terms) need to be at most quadratic in the gradients, on the other they can even grow arbitrarily provided that they do not \oscillate extremely much in the space variable" (a conditions expressed rigorously by means of certain inequalities that involve the space derivatives of the Hamiltonians). We concentrate on periodic conditions, but the same techniques allow to handle Dirichlet, Neumann...boundary conditions, or even the evolutive counterpart of these equations.
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hal-01068708 , version 1 (26-09-2014)


  • HAL Id : hal-01068708 , version 1


Martino Bardi, Ermal Feleqi. Nonlinear elliptic systems and mean eld games. 2014. ⟨hal-01068708⟩
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