Evolutionary, symmetric \(p\)-Laplacian. Interior regularity of time derivatives and its consequences. (English) Zbl 1362.35160
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.
Reviewer: Josef Diblík (Brno)
MSC:
| 35K59 | Quasilinear parabolic equations |
| 35K55 | Nonlinear parabolic equations |
| 35K92 | Quasilinear parabolic equations with \(p\)-Laplacian |
| 35Q35 | PDEs in connection with fluid mechanics |
| 35B65 | Smoothness and regularity of solutions to PDEs |
Keywords:
evolutionary systems of PDEs; symmetric \(p\)-Laplacian; local (interior) regularity of time derivatives; iteration in Nikolskii-Bochner spacesReferences:
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