6533b874fe1ef96bd12d629b

RESEARCH PRODUCT

Convergence of dynamic programming principles for the $p$-Laplacian

Juan J. ManfrediFélix Del TesoMikko Parviainen

subject

equivalent notions of solutions01 natural sciencesMathematics - Analysis of PDEsnumerical methodsConvergence (routing)FOS: MathematicsApplied mathematicsgeneralized viscosity solutiondiscrete approximationsMathematics - Numerical Analysis0101 mathematicsGeometry and topologyDirichlet problemMathematicsviscosity solutionosittaisdifferentiaaliyhtälötDirichlet problemasymptotic mean value propertiesconvergencenumeeriset menetelmätApplied Mathematics010102 general mathematicsNumerical Analysis (math.NA)dynamic programming principle010101 applied mathematicsDynamic programmingp-Laplacianmonotone approximationsapproksimointiAnalysisAnalysis of PDEs (math.AP)

description

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.

yearjournalcountryeditionlanguage
2018-08-30
http://arxiv.org/abs/1808.10154