A pointwise estimate of the solution to the pp-Laplace evolution equation

In the cylinder (BR∖F¯)×(0,T) we consider the Dirichlet problem for the pp-Laplace evolution equation. Here FF is an open set of diameter dd, BR⊂RnBR⊂Rn is an open ball of radius R=R(T,d,p)R=R(T,d,p), dd is small enough, and p∈(2nn+1,2]. Using Moser’s iterative procedure, we derive the pointwise estimates for the solution of this problem in terms of the diameter of the set FF.