Asymptotic mean value formulas for parabolic nonlinear equations. (English) Zbl 1503.35102
Summary: In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge-Ampère equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from a probabilistic point of view in terms of dynamic programming principles for certain two-player, zero-sum games.
MSC:
| 35K96 | Parabolic Monge-Ampère equations |
| 35D40 | Viscosity solutions to PDEs |
| 35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |
Keywords:
asymptotic mean value formulas; viscosity solutions; parabolic nonlinear equations; parabolic Monge-Ampère equationsReferences:
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