At page 5 (125), seven line after the Proof of Theorem 2.2(i), of the following article.
THE HEAT EQUATION WITH A SINGULAR POTENTIAL
the authors say that since $p$ is convex, we can deduce that
$$ \int_{\delta}^{t} \int_{\Omega} p(u_n) (- \Delta \phi) \leq \int_{\delta}^{t} \int_{\Omega} \nabla u_n \cdot \nabla (\phi \, p'(u_n)). $$
I am confused about how convexity is used. I will be thanked if anyone could help me.
