A new short proof of regularity for local weak solutions for a certain class of singular parabolic equations

We shall establish the interior Holder continuity for locally bounded weak solutions to a class of parabolic singular equations whose prototypes are u_t = ∇ · (|∇u|^(p−2)∇u), for 1 < p < 2, and u_t − ∇ · (u^(m−1)|∇u|^(p−2)∇u) = 0, for m + p > 3 −p/N via a new and simplified proof using recent techniques on expansion of positivity and L1-Harnack estimates