Expansion of positivity to a class of doubly nonlinear parabolic equations

Abstract

We establish the expansion of positivity of the nonnegative, local, weak solutions to the class of doubly nonlinear parabolic equations ∂ t ( u q ) − div ⁡ ( | D u | p − 2 D u ) = 0 ,   p > 1   and   q > 0 considering separately the two possible cases q + 1 − p > 0 and q + 1 − p < 0 . The proof relies on the procedure presented by DiBenedetto, Gianazza and Vespri for both the degenerate and the singular parabolic p -Laplacian equation.