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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| Autores principales: | , , |
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| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00222518_v63_n4_p1067_Mazon |
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| Sumario: | 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 © |
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