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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 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.

Registro:

Documento: Artículo
Título:On the best Lipschitz extension problem for a discrete distance and the discrete ∞-Laplacian
Autor:Mazón, J.M.; Rossi, J.D.; Toledo, J.
Filiación:Departament d'Anàlisi Matemàtica, Universitat de València, Valencia, Spain
Departamento de Análisis Matemático, Universidad de Alicante, Ap. correos 99, 03080, Alicante, Spain
Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina
Palabras clave:Infinity laplacian; Lipschitz extension; Nonlocal p-Laplacian problem; Tug-of-war games
Año:2012
Volumen:97
Número:2
Página de inicio:98
Página de fin:119
DOI: http://dx.doi.org/10.1016/j.matpur.2011.09.003
Título revista:Journal des Mathematiques Pures et Appliquees
Título revista abreviado:J. Math. Pures Appl.
ISSN:00217824
CODEN:JMPAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217824_v97_n2_p98_Mazon

Referencias:

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Citas:

---------- APA ----------
Mazón, J.M., Rossi, J.D. & Toledo, J. (2012) . On the best Lipschitz extension problem for a discrete distance and the discrete ∞-Laplacian. Journal des Mathematiques Pures et Appliquees, 97(2), 98-119.
http://dx.doi.org/10.1016/j.matpur.2011.09.003
---------- CHICAGO ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "On the best Lipschitz extension problem for a discrete distance and the discrete ∞-Laplacian" . Journal des Mathematiques Pures et Appliquees 97, no. 2 (2012) : 98-119.
http://dx.doi.org/10.1016/j.matpur.2011.09.003
---------- MLA ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "On the best Lipschitz extension problem for a discrete distance and the discrete ∞-Laplacian" . Journal des Mathematiques Pures et Appliquees, vol. 97, no. 2, 2012, pp. 98-119.
http://dx.doi.org/10.1016/j.matpur.2011.09.003
---------- VANCOUVER ----------
Mazón, J.M., Rossi, J.D., Toledo, J. On the best Lipschitz extension problem for a discrete distance and the discrete ∞-Laplacian. J. Math. Pures Appl. 2012;97(2):98-119.
http://dx.doi.org/10.1016/j.matpur.2011.09.003