Functions of least gradient and 1-harmonic functions
In this paper, we find the Euler-Lagrange equation corresponding to functions of least gradient. It turns out that this equation can be identified with the 1-Laplacian. Moreover, given a Lipschitz domain Ω, we prove that there exists a function of least gradient in Ω that extends every datum belongi...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00222518_v63_n4_p1067_Mazon |
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todo:paper_00222518_v63_n4_p1067_Mazon2023-10-03T14:29:55Z Functions of least gradient and 1-harmonic functions Mazón, J.M. Rossi, J.D. De León, S.S. 1-Laplacian Functions of least gradient In this paper, we find the Euler-Lagrange equation corresponding to functions of least gradient. It turns out that this equation can be identified with the 1-Laplacian. Moreover, given a Lipschitz domain Ω, we prove that there exists a function of least gradient in Ω that extends every datum belonging to L1 (∂ Ω). We show, as well, the non-uniqueness of solutions in the case of discontinuous boundary values. Indiana University Mathematics Journal © 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_00222518_v63_n4_p1067_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 Functions of least gradient |
| spellingShingle |
1-Laplacian Functions of least gradient Mazón, J.M. Rossi, J.D. De León, S.S. Functions of least gradient and 1-harmonic functions |
| topic_facet |
1-Laplacian Functions of least gradient |
| description |
In this paper, we find the Euler-Lagrange equation corresponding to functions of least gradient. It turns out that this equation can be identified with the 1-Laplacian. Moreover, given a Lipschitz domain Ω, we prove that there exists a function of least gradient in Ω that extends every datum belonging to L1 (∂ Ω). We show, as well, the non-uniqueness of solutions in the case of discontinuous boundary values. Indiana University Mathematics Journal © |
| format |
JOUR |
| author |
Mazón, J.M. Rossi, J.D. De León, S.S. |
| author_facet |
Mazón, J.M. Rossi, J.D. De León, S.S. |
| author_sort |
Mazón, J.M. |
| title |
Functions of least gradient and 1-harmonic functions |
| title_short |
Functions of least gradient and 1-harmonic functions |
| title_full |
Functions of least gradient and 1-harmonic functions |
| title_fullStr |
Functions of least gradient and 1-harmonic functions |
| title_full_unstemmed |
Functions of least gradient and 1-harmonic functions |
| title_sort |
functions of least gradient and 1-harmonic functions |
| url |
http://hdl.handle.net/20.500.12110/paper_00222518_v63_n4_p1067_Mazon |
| work_keys_str_mv |
AT mazonjm functionsofleastgradientand1harmonicfunctions AT rossijd functionsofleastgradientand1harmonicfunctions AT deleonss functionsofleastgradientand1harmonicfunctions |
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1807318175257198592 |