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January/February 2009 Very weak solutions of higher-order degenerate parabolic systems
Verena Bögelein
Adv. Differential Equations 14(1/2): 121-200 (January/February 2009).

Abstract

We consider non-linear higher-order parabolic systems whose simplest model is the parabolic $p$-Laplacean system \begin{equation*} \int_{\Omega_T} u\cdot \varphi_t - \langle |D^mu|^{p-2}D^mu,D^m\varphi\rangle \,dz = 0. \end{equation*} It turns out that the usual regularity assumptions on solutions can be weakened in the sense that going slightly below the natural integrability exponent still yields a classical weak solution. Namely, we prove the existence of some $\beta>0$ such that $D^mu\in L^{p-\beta} \Rightarrow D^mu\in L^{p+\beta}$.

Citation

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Verena Bögelein. "Very weak solutions of higher-order degenerate parabolic systems." Adv. Differential Equations 14 (1/2) 121 - 200, January/February 2009.

Information

Published: January/February 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1178.35215
MathSciNet: MR2478931

Subjects:
Primary: 35D10, 35G20, 35K65

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.14 • No. 1/2 • January/February 2009
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