On the second-order regularity of solutions to the parabolic p-Laplace equation

Abstract In this paper, we study the second-order Sobolev regularity of solutions to parabolic p -Laplace equation. For any -parabolic function u , show that $$D(\left| Du\right| ^{\frac{p-2+s}{2}}Du)$$ D ( u p - 2 + s ) exists as a and belongs $$L^{2}_{\text {loc}}$$ L loc with $$s>-1$$ > 1 $$1<p<\infty $$ < ∞ . The range s is sharp.