I was reading Ricci flow: Techniques and Applications (Part - II: Analytic Aspects) by B. Chow et al. In Chapter $14$ section $6$ there is an exercise stating:
Exercise $14.24$: Prove higher derivative Bernstein-type estimates for the local heat equation.
I was unable to find any reference online to deal the problem. I could not understand the term "higher derivative estimates".
Can somebody provide me an example or article related to this type of estimation (involving higher derivatives)? In addition if some applications (like how to derive Harnack inequality for this estimation) can be provided then it would be very helpful.