Equivalence of viscosity and weak solutions for a p-parabolic equation

Abstract We study the relationship of viscosity and weak solutions to equation $$\begin{aligned} \smash {\partial _{t}u-\varDelta _{p}u=f(Du)}, \end{aligned}$$ ? t u - ? p = f ( D ) , where $$p>1$$ > 1 $$f\in C({\mathbb {R}}^{N})$$ ? C R N satisfies suitable assumptions. Our main result is that bounded supersolutions coincide with lower semicontinuous supersolutions. Moreover, we prove semicontinuity when $$p\ge 2$$ ? 2 .