Hölder continuity of local weak solutions for parabolic equations exhibiting two degeneracies

Abstract

We consider equations of the form atv - div(Q ( v)Vv) == 0 , where v E [0,1] and Q(v) degenerates for v == 0 and v == 1. We show that local weak solutions are locally Holder continuous provided Q behaves like a power near the two degeneracies. We adopt the technique of intrinsic rescaling developed by DiBenedetto.