That is, there holds strong maximum principle for solutions of $u_t- \Delta_p u=0$? I know that it holds for caloric functions, that is, for solutions of $u_t- \Delta u=0$. A priori, I don't want to know specifically about some type of SMP. So if you know any type under any sense of solution or conditions, please let me know or give references.
An SMP that I think would reasonably hold would be: if u is a non-negative solution of $u_t-\Delta_p u= 0$ in $\Omega \times (0,R)$ with $u(0,0) = 0$ then
i) there exists an r>0 such that $u\equiv 0$ in $\Omega \times (0,r)$ or else it would hold at least ii) $u(x,0) \equiv 0$
It is likely that a result of this type holds or not depending on whether the equation is degenerate $p=2$ or singular $1<p<2$.
I already asked this question at mathstackexchange, however, even with a bounty I do not see answers.
