6533b7dcfe1ef96bd1272a96
RESEARCH PRODUCT
Solutions of nonlinear PDEs in the sense of averages
Juan J. ManfrediMikko ParviainenBernd Kawohlsubject
Class (set theory)Mean value theoremMathematics(all)Dynamic programming principleGeneral MathematicsAsymptotic expansion01 natural sciences1-harmonicApplied mathematics0101 mathematicsMathematicsp-harmonicApplied Mathematics010102 general mathematicsMathematical analysista111Zero (complex analysis)Sense (electronics)010101 applied mathematicsNonlinear systemRange (mathematics)Two-player zero-sum gamesMean value theorem (divided differences)Viscosity solutionsAsymptotic expansionValue (mathematics)Stochastic gamesdescription
Abstract We characterize p-harmonic functions including p = 1 and p = ∞ by using mean value properties extending classical results of Privaloff from the linear case p = 2 to all pʼs. We describe a class of random tug-of-war games whose value functions approach p-harmonic functions as the step goes to zero for the full range 1 p ∞ .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-02-01 | Journal de Mathématiques Pures et Appliquées |