American Institute of Mathematical Sciences

January  2015, 14(1): 167-184. doi: 10.3934/cpaa.2015.14.167

General existence of solutions to dynamic programming equations

 1 Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260 2 Max-Planck Institut MiS Leipzig, Inselstr. 22, 04103 Leipzig, Germany

Received  December 2013 Revised  January 2014 Published  September 2014

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.
Citation: Qing Liu, Armin Schikorra. General existence of solutions to dynamic programming equations. Communications on Pure & Applied Analysis, 2015, 14 (1) : 167-184. doi: 10.3934/cpaa.2015.14.167
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