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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Detalles Bibliográficos
Autor principal: Rossi, Julio Daniel
Publicado: 2014
Materias:
1-Laplacian
Functions of least gradient
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222518_v63_n4_p1067_Mazon
http://hdl.handle.net/20.500.12110/paper_00222518_v63_n4_p1067_Mazon
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00222518_v63_n4_p1067_Mazon
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spelling paper:paper_00222518_v63_n4_p1067_Mazon2023-06-08T14:48:22Z Functions of least gradient and 1-harmonic functions Rossi, Julio Daniel 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. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222518_v63_n4_p1067_Mazon 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
Rossi, Julio Daniel
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 ©
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
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
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222518_v63_n4_p1067_Mazon
http://hdl.handle.net/20.500.12110/paper_00222518_v63_n4_p1067_Mazon
work_keys_str_mv AT rossijuliodaniel functionsofleastgradientand1harmonicfunctions
_version_ 1768541973001535488

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