Asymptotic mean value properties for the P-Laplacian

Abstract

The purpose of this article is to obtain mean value characterizations of solutions to some nonlinear PDEs. To motivate the results we review some recent results concerning Tug-of-War games and their relation with PDEs. In particular, we will show that solutions to certain PDEs can be obtained as limits of values of Tug-of-War games when the parameter that controls the length of the possible movements goes to zero. Since the equations under study are nonlinear and not in divergence form we will make extensive use of the concept of viscosity solutions.

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Correspondence to J. D. Rossi.

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Rossi, J.D. Asymptotic mean value properties for the P-Laplacian. SeMA 56, 35–62 (2011). https://doi.org/10.1007/BF03322596

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Key words

  • Mean value properties
  • Tug-of-War games
  • viscosity solutions

AMS subject classifications

  • 35J60
  • 91A05
  • 49L25
  • 35J25