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In recent years there has been an increasing interest in whether a mean value property, known to characterize harmonic functions, can be extended in some weak form to solutions of nonlinear equations. This question has been partially motivated by the surprising connection between Random Tug-of-War games and the normalized p-Laplacian discovered some years ago by Peres et al., where a nonlinear asymptotic mean value property for solutions of a PDE is related to a dynamic programming principle for an appropriate game. In this talk, we discuss asymptotic mean value formulas for a class of nonlinear second-order equations that includes the classical Monge-Ampère and k-Hessian equations among other examples.
Asymptotic Mean Value Formulas for Nonlinear Equations Sponsored by the Meyer Fund
Asymptotic Mean Value Formulas for Nonlinear Equations