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Mazon, J.M.; Perez-Llanos, M.; Rossi, J.D.; Toledo, J. "A nonlocal 1-laplacian problem and median values" (2016) Publicacions Matematiques. 60:27-53
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Abstract:

In this paper, we study solutions to a nonlocal 1-Laplacian equation given by [EQUATION PRESENTED] with u(x) = ψ (x) for x 2 ∈ ωJ\\ω. We introduce two notions of solution and prove that the weaker of the two concepts is equivalent to a nonlocal median value property, where the median is determined by a measure related to J. We also show that solutions in the stronger sense are nonlocal analogues of local least gradient functions, in the sense that they minimize a nonlocal functional. In addition, we prove that solutions in the stronger sense converge to least gradient solutions when the kernel J is appropriately rescaled.

Registro:

Documento: Artículo
Título:A nonlocal 1-laplacian problem and median values
Autor:Mazon, J.M.; Perez-Llanos, M.; Rossi, J.D.; Toledo, J.
Filiación:Departament d'Analisi Matematica, Universitat de Valencia, Dr. Moliner 50, Burjassot, 46100, Spain
Departamento de Matematicas, Universidad Autonoma de Madrid, Campus de Cantoblanco, Facultad de Ciencias, mod 17, Madrid, 28049, Spain
Departamento de Matematica, FCEyN UBA, Ciudad Universitaria, Buenos Aires, 1428, Argentina
Palabras clave:1-Laplacian; Least gradient functions; Median value
Año:2016
Volumen:60
Página de inicio:27
Página de fin:53
DOI: http://dx.doi.org/10.5565/PUBLMAT_60116_02
Título revista:Publicacions Matematiques
Título revista abreviado:Publ. Mat.
ISSN:02141493
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02141493_v60_n_p27_Mazon

Referencias:

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Citas:

---------- APA ----------
Mazon, J.M., Perez-Llanos, M., Rossi, J.D. & Toledo, J. (2016) . A nonlocal 1-laplacian problem and median values. Publicacions Matematiques, 60, 27-53.
http://dx.doi.org/10.5565/PUBLMAT_60116_02
---------- CHICAGO ----------
Mazon, J.M., Perez-Llanos, M., Rossi, J.D., Toledo, J. "A nonlocal 1-laplacian problem and median values" . Publicacions Matematiques 60 (2016) : 27-53.
http://dx.doi.org/10.5565/PUBLMAT_60116_02
---------- MLA ----------
Mazon, J.M., Perez-Llanos, M., Rossi, J.D., Toledo, J. "A nonlocal 1-laplacian problem and median values" . Publicacions Matematiques, vol. 60, 2016, pp. 27-53.
http://dx.doi.org/10.5565/PUBLMAT_60116_02
---------- VANCOUVER ----------
Mazon, J.M., Perez-Llanos, M., Rossi, J.D., Toledo, J. A nonlocal 1-laplacian problem and median values. Publ. Mat. 2016;60:27-53.
http://dx.doi.org/10.5565/PUBLMAT_60116_02