General Existence of Solutions to Dynamic Programming Principle

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.

References in corpus (1)

• An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions

Cited by in corpus (2)

• The evolution problem associated with eigenvalues of the Hessian
• A game theoretical approach for an elliptic system with two different operators (the Laplacian and the infinity Laplacian)