Transition of Electric field and potential between media

[Gavroy]

I am interested in the main difference between transitions from electric fields from Conductive to Conductive/ Dielectric to Dielectric and Dielectric/Conductive media.

What are the boundary conditions that an Electric field and a potential has to fulfill?
I think I only know it for dielectric to dielectric media, where the potential has to be continuous and the electric field changes by the amount of surface charge.

Could somebody comment on the behavior and maybe use or refer to some equations?

 

[DrDu]

Take the metal as a dielectric whose dielectric constant approaches infinity. What boundary conditions do you get in this limit?