# Convergence of dynamic programming principles for the p-Laplacian

@article{delTeso2018ConvergenceOD, title={Convergence of dynamic programming principles for the p-Laplacian}, author={F{\'e}lix del Teso and Juan J. Manfredi and Mikko Parviainen}, journal={Advances in Calculus of Variations}, year={2018}, volume={15}, pages={191 - 212} }

Abstract We provide a unified strategy to show that solutions of dynamic programming principles associated to the p-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for continuous and discrete dynamic programming principles, provides new results, and gives a convergence proof free of probability arguments.

## 17 Citations

### Convergence of the natural p-means for the p-Laplacian

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### Convergence of Natural $p$-Means for the $p$-Laplacian in the Heisenberg Group

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We introduce games associated with second-order partial differential equations given by arbitrary products of eigenvalues of the Hessian. We prove that, as a parameter that controls the step length…

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### Boundary Aware Tug-of-War with Noise: Case p ∈ (2, ∞)

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- 2020

This chapter improves on the construction of the Tug-of-War game in Chap. 3 and proves convergence of its values to p-harmonic functions, in the simplified nondegenerate case. This first convergence…

### An asymptotic expansion for the fractional p-Laplacian and for gradient-dependent nonlocal operators

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Mean value formulas are of great importance in the theory of partial differential equations: many very useful results are drawn, for instance, from the well known equivalence between harmonic…

### A Finite Difference Method for the Variational p-Laplacian

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### Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph infinity Laplacian

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### On the Weak Convergence of Monge-Ampère Measures for Discrete Convex Mesh Functions

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A discrete Aleksandrov-Bakelman-Pucci's maximum principle is derived and it is used to prove the weak convergence of Monge-Ampere measures for discrete convex mesh functions, converging uniformly on compact subsets, interpolating boundary values of a continuous convex function and withMonge- Ampere masses uniformly bounded.

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