Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 33, 2008, 387-412

HIGHER INTEGRABILITY FOR WEAK SOLUTIONS OF HIGHER ORDER DEGENERATE PARABOLIC SYSTEMS

Verena Bögelein

Universität Erlangen-Nürnberg, Department Mathematik
Bismarckstrasse 1 1/2, 91054 Erlangen, Germany; boegelein 'at' mi.uni-erlangen.de

Abstract. We consider a class of higher order nonlinear degenerate parabolic systems, whose easiest model is the parabolic p-Laplacean system

\int_{\Omega_T} (u \cdot \varphi_t - |D^mu|^p-2D^mu \cdot D^m\varphi) dz = \int_{\Omega_T} \sum_k=0^m-1 B^k(\cdot,D^mu) \cdot D^k\varphi dz

and show higher integrability for weak solutions, proving that D^mu \in L^p implies that D^mu \in L^p+\epsilon for some \epsilon > 0.

2000 Mathematics Subject Classification: Primary 35D10, 35G20, 35K65.

Key words: Higher integrability, degenerate parabolic systems, higher order, parabolic p-Laplacean.

Reference to this article: V. Bögelein: Higher integrability for weak solutions of higher order degenerate parabolic systems. Ann. Acad. Sci. Fenn. Math. 33 (2008), 387-412.

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