6533b828fe1ef96bd12885b6

RESEARCH PRODUCT

On the best Lipschitz extension problem for a discrete distance and the discrete ∞-Laplacian

Julio D. RossiJosé M. MazónJulián Toledo

subject

Discrete mathematicsMathematics(all)General MathematicsApplied MathematicsMathematics::Analysis of PDEsTug-of-war gamesExtension (predicate logic)Lipschitz continuityDynamic programmingLipschitz domainBellman equationInfinity LaplacianNonlocal p-Laplacian problemLimit (mathematics)Lipschitz extensionLaplacian matrixLaplace operatorMathematics

description

Abstract This paper concerns the best Lipschitz extension problem for a discrete distance that counts the number of steps. We relate this absolutely minimizing Lipschitz extension with a discrete ∞-Laplacian problem, which arises as the dynamic programming formula for the value function of some e -tug-of-war games. As in the classical case, we obtain the absolutely minimizing Lipschitz extension of a datum f by taking the limit as p → ∞ in a nonlocal p -Laplacian problem.

yearjournalcountryeditionlanguage
2012-02-01Journal de Mathématiques Pures et Appliquées
10.1016/j.matpur.2011.09.003http://dx.doi.org/10.1016/j.matpur.2011.09.003