General Existence of Solutions to Dynamic Programming Principle

Qing Liu and Armin Schikorra

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Submission date: 16. Aug. 2013
published in: Communications on pure and applied analysis, 14 (2015) 1, p. 167-184 
DOI number (of the published article): 10.3934/cpaa.2015.14.167
Bibtex
with the following different title: General existence of solutions to dynamic programming equations
MSC-Numbers: 35A35, 49C20, 91A05

Abstract:
We provide an alternative approach to the existence of solutions to dynamic programming equations arising in the discrete game-theoretic interpretations for various nonlinear partial differential equations including the infinity Laplacian, mean curvature flow and Hamilton-Jacobi type. Our general result is similar to Perron's method but adapted to the discrete situation.