This article is cited in 5 papers

On the regularity of the solutions of the Neumann problem for quasilinear parabolic systems

A. A. Arkhipova

Saint-Petersburg State University

Abstract: Partial regularity is proved of the generalized solution $u\colon\mathbf\Omega\times(0,T)\to\mathbf R^N$, $\mathbf\Omega\subset\mathbf R^n$, $n>2$, $N>1$, of a quasilinear parabolic system with nonsmooth conormal derivative. It is assumed that the functions forming the system and the boundary condition have controlled orders of nonlinearities, and their singularities are anisotropic with respect to the spatial variables and time. $L_p$-estimates of the gradient of $u$ in a neighborhood of $\partial\mathbf\Omega\times(0,T)$ are preliminarily deduced.

UDC: 517.953

MSC: 35K20, 35K60, 35B65

Received: 20.10.1993

 English version: Russian Academy of Sciences. Izvestiya Mathematics, 1995, 45:2, 231–253

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