Abstract
We consider an evolutionary, non-degenerate, symmetric p-Laplacian. By symmetric we mean that the full gradient of p-Laplacian is replaced by its symmetric part, which causes a breakdown of the Uhlenbeck structure.
We derive interior regularity of time derivatives of its local weak solution. To circumvent the space-time growth mismatch, we devise a new local regularity technique of iterations in Nikolskii-Bochner spaces.
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. Finally, having our regularity result for time derivatives, we obtain respective regularity of the main part.
The Appendix on Nikolskii-Bochner spaces, that includes theorems on their embeddings and interpolations, may be of independent interest.