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arXiv · 2107.00743

A Hessian-dependent functional with free boundaries and applications to mean-field games

Julio C. Correa·Edgard A. Pimentel
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Abstract

We study a Hessian-dependent functional driven by a fully nonlinear operator. The associated Euler-Lagrange equation is a fully nonlinear mean-field game with free boundaries. Our findings include the existence of solutions to the mean-field game, together with H\"older continuity of the value function and improved integrability of the density. In addition, we prove the reduced free boundary is a set of finite perimeter. To conclude our analysis, we prove a $\Gamma$-convergence result for the functional.

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Julio C. Correa, Edgard A. Pimentel. 2021-07-01. A Hessian-dependent functional with free boundaries and applications to mean-field games. https://arxiv.org/abs/2107.00743

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