A nonlocal 1-laplacian problem and median values
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 b...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_02141493_v60_n_p27_Mazon |
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todo:paper_02141493_v60_n_p27_Mazon2023-10-03T15:10:12Z A nonlocal 1-laplacian problem and median values Mazon, J.M. Perez-Llanos, M. Rossi, J.D. Toledo, J. 1-Laplacian Least gradient functions Median value 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. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_02141493_v60_n_p27_Mazon |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
1-Laplacian Least gradient functions Median value |
| spellingShingle |
1-Laplacian Least gradient functions Median value Mazon, J.M. Perez-Llanos, M. Rossi, J.D. Toledo, J. A nonlocal 1-laplacian problem and median values |
| topic_facet |
1-Laplacian Least gradient functions Median value |
| description |
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. |
| format |
JOUR |
| author |
Mazon, J.M. Perez-Llanos, M. Rossi, J.D. Toledo, J. |
| author_facet |
Mazon, J.M. Perez-Llanos, M. Rossi, J.D. Toledo, J. |
| author_sort |
Mazon, J.M. |
| title |
A nonlocal 1-laplacian problem and median values |
| title_short |
A nonlocal 1-laplacian problem and median values |
| title_full |
A nonlocal 1-laplacian problem and median values |
| title_fullStr |
A nonlocal 1-laplacian problem and median values |
| title_full_unstemmed |
A nonlocal 1-laplacian problem and median values |
| title_sort |
nonlocal 1-laplacian problem and median values |
| url |
http://hdl.handle.net/20.500.12110/paper_02141493_v60_n_p27_Mazon |
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1807324476679913472 |