Games associated with products of eigenvalues of the Hessian. (English) Zbl 1541.35512
Summary: We introduce games associated with second-order partial differential equations given by arbitrary products of eigenvalues of the Hessian. We prove that, as a parameter that controls the step length goes to zero, the value functions of the games converge uniformly to a viscosity solution of the partial differential equation. The classical Monge-Ampère equation is an important example under consideration.
MSC:
| 35Q91 | PDEs in connection with game theory, economics, social and behavioral sciences |
| 91A05 | 2-person games |
| 35J96 | Monge-Ampère equations |
| 35D40 | Viscosity solutions to PDEs |
| 35P15 | Estimates of eigenvalues in context of PDEs |
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