An Asymptotic Mean Value Characterization for a Class of Nonlinear Parabolic Equations Related to Tug-of-War Games

@article{Manfredi2010AnAM,
  title={An Asymptotic Mean Value Characterization for a Class of Nonlinear Parabolic Equations Related to Tug-of-War Games},
  author={Juan J. Manfredi and Mikko Parviainen and Julio D. Rossi},
  journal={SIAM J. Math. Anal.},
  year={2010},
  volume={42},
  pages={2058-2081}
}
We characterize solutions to the homogeneous parabolic p-Laplace equation $u_{t}=|\nabla u|^{2-p}\Delta_{p}u=(p-2)\Delta_{\infty}u+\Delta u$ in terms of an asymptotic mean value property. The results are connected with the analysis of tug-of-war games with noise in which the number of rounds is bounded. The value functions for these games approximate a solution to the PDE above when the parameter that controls the size of the possible steps goes to zero. 

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