In this paper, we study existence of solutions to the $1$--Laplacian elliptic equation with inhomogeneous Robin boundary conditions. It is also analyzed from the point of view of the Euler--Lagrange equation of a lower semicontinuous functional. We see the equivalence between the solutions of the elliptic problem and the minimizers of the functional.
"The $1$--Laplacian elliptic equation with inhomogeneous Robin boundary conditions." Differential Integral Equations 28 (5/6) 401 - 430, May/June 2015.