# Weak solutions for first order mean field games with local coupling

Abstract : Existence and uniqueness of a weak solution for first order mean field game systems with local coupling are obtained by variational methods. This solution can be used to devise $\epsilon-$Nash equilibria for deterministic differential games with a finite (but large) number of players. For smooth data, the first component of the weak solution of the MFG system is proved to satisfy (in a viscosity sense) a time-space degenerate elliptic differential equation.
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https://hal.archives-ouvertes.fr/hal-00827957
Contributor : Pierre Cardaliaguet <>
Submitted on : Thursday, May 30, 2013 - 8:38:25 AM
Last modification on : Wednesday, September 23, 2020 - 4:30:49 AM
Long-term archiving on: : Saturday, August 31, 2013 - 4:15:54 AM

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MFG1ordre2013_05_28.pdf
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### Identifiers

• HAL Id : hal-00827957, version 1
• ARXIV : 1305.7015

### Citation

Pierre Cardaliaguet. Weak solutions for first order mean field games with local coupling. Bettiol, P., Cannarsa, P., Colombo, G., Motta, M., & Rampazzo, F. Analysis and Geometry in Control Theory and its Applications., 11, 2015, Springer INdAM Series. ⟨hal-00827957⟩

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