General existence of solutions to dynamic programming equations

Qing Liu; Armin Schikorra

doi:10.3934/cpaa.2015.14.167

Article Contents

2015, Volume 14, Issue 1: 167-184. Doi: 10.3934/cpaa.2015.14.167

This issue Previous Article Convergence of equilibria for incompressible elastic plates in the von Kármán regime Next Article Mean value properties and unique continuation

General existence of solutions to dynamic programming equations

Qing Liu^1, and
Armin Schikorra^2,

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

Received: November 30, 2013

Revised: December 31, 2013

Published: December 2014

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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.

Keywords:

Dynamic programming principle,
differential games,
nonlinear partial differential equations.

Mathematics Subject Classification: 35A35, 49C20, 91A05, 91A15.

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