The strong maximum principle in parabolic problems with the p-Laplacian in a domain

We establish a strong maximum principle for a nonnegative continuous solution u:Ω¯×[0,T)→R+ of a doubly nonlinear parabolic problem in a space-time cylinder Ω×(0,τ) with a domain Ω⊂RN and a sufficiently short time interval (0,τ)⊂(0,T). Our method takes advantage of a nonnegative subsolution derived from an expanding spherical wave.