A comparison among various notions of viscosity solution for Hamilton–Jacobi equations on networks

Three definitions of viscosity solutions for Hamilton–Jacobi equations on networks recently appeared in literature (Achdou et al. (2013) [1], Imbert et al. (2013) [4], Schieborn and Camilli (2013) [6]). Being motivated by various applications, they appear to be considerably different. The aim of this note is to establish their equivalence.