Dirichlet boundary conditions for degenerate and singular nonlinear   parabolic equations
  We study existence and uniqueness of solutions to a class of nonlinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To this purpose some barrier functions are properly introduced and used. 
Fabio Punzo, Marta Strani
math.AP