Energy solutions to one-dimensional singular parabolic problems with   $BV$ data are viscosity solutions
  We study one-dimensional very singular parabolic equations with periodic boundary conditions and initial data in $BV$, which is the energy space. We show existence of solutions in this energy space and then we prove that they are viscosity solutions in the sense of Giga-Giga. 
Atsushi Nakayasu, Piotr Rybka
math.AP