Gorenstein injective, Gorenstein flat modules and the section functor

Let RR be a commutative Noetherian ring of Krull dimension dd, and let aa be an ideal of RR. In this paper, we will study the strong cotorsioness and the Gorenstein injectivity of the section functor Γa(−)Γa(−) in local cohomology. As applications, we will find new characterizations for Gorenstein and regular local rings. We also study the effect of the section functors Γa(−)Γa(−) and the functors Had(−) on the Auslander and Bass classes.