Evolutionary, symmetric \(p\)-Laplacian. Interior regularity of time derivatives and its consequences (Q334519)

An evolutionary, non-degenerate, symmetric \(p\)-Laplacian is considered. Interior regularity of time derivatives of its local weak solution is proven. A new local regularity technique of iterations in Nikolskii-Bochner spaces is proposed (it is interesting by itself, as it may be modified to provide new regularity results for the full-gradient p-Laplacian case with lower-order dependencies). Using the regularity result for the time derivatives, regularity of the main part is derived. The appendix on Nikolskii-Bochner spaces (including theorems on their embeddings and interpolations) is of independent interest.