I think I understood how to apply Fichera criteria to the Black Scholes type of equation and I see it is mentioned it was originally developed for elliptic type of equations. We can consider BS eq as elliptic such that it degenerates for all t and therefore we need terminal condition for t=T.
However, what about transport equation say u_t+u_x=0? This is not elliptic but can it be considered one by arguing that it degenerates for all t and for all x and therefore we need to calculate the Fichera function?
I thought "degenerate" meant to define some points(regions) that lower the order of the equation from n to n-1 but that transport equation I have written is of first order to begin with and it doesn't degenerate at any x. Or, shall I say the Fichera theory only applies to those degenerate equations such that happen to become of order 1 from 2 at certain points in the region? So that transport equation could be of order 2?