The $1$--Laplacian elliptic equation with inhomogeneous Robin boundary conditions
José M. Mazón, Julio Daniel Rossi, Sergio Segura de León · Differential and Integral Equations · 2015
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.