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

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 ε-tug-of-war...

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Detalles Bibliográficos
Autores principales: Mazón, J.M., Rossi, J.D., Toledo, J.
Formato: JOUR
Materias:
Infinity laplacian
Lipschitz extension
Nonlocal p-Laplacian problem
Tug-of-war games
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00217824_v97_n2_p98_Mazon
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario: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 ε-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. © 2011 Elsevier Masson SAS.

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