Functions of least gradient and 1-harmonic functions
J. M. MazonJulio RossiS. Segura de Leon
35J7535J2035J9235J25Functions of least gradient1-Laplacian
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 $\Omega$, we prove that there exists a function of least gradient in $\Omega$ that extends every datum belonging to $L^1(\partial\Omega)$. We show, as well, the non-uniqueness of solutions in the case of discontinuous boundary values.
Indiana University Mathematics Journal
2014
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10.1512/iumj.2014.63.5327
10.1512/iumj.2014.63.5327
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Indiana Univ. Math. J. 63 (2014) 1067 - 1084
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