
Journal of Convex Analysis 28 (2021), No. 2, [final page numbers not yet available] Copyright Heldermann Verlag 2021 A Nonlinear Mean Value Property for the MongeAmpère Operator Pablo Blanc Dept. of Mathematics and Statistics, University of Jyväskylä, Finland pblanc@dm.uba.ar Fernando Charro Department of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A. fcharro@wayne.edu Juan J. Manfredi Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A. manfredi@pitt.edu Julio D. Rossi Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Argentina jrossi@dm.uba.ar 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 TugofWar games and the normalized pLaplacian discovered some years ago, where a nonlinear asymptotic mean value property for solutions of a PDE is related to a dynamic programming principle for an appropriate game. Currently, asymptotic nonlinear mean value formulas are rare in the literature and our goal is to show that an asymptotic nonlinear mean value formula holds for the classical MongeAmpère equation. Keywords: MongeAmpere, Mean Value Formulas, viscosity solutions. MSC: 35J60, 35J96, 35B05. [ Fulltextpdf (208 KB)] for subscribers only. 