Advances in Differential Equations

Very weak solutions of higher-order degenerate parabolic systems

Verena Bögelein

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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 $D^mu\in L^{p-\beta} \Rightarrow D^mu\in L^{p+\beta}$.

Article information

Adv. Differential Equations, Volume 14, Number 1/2 (2009), 121-200.

First available in Project Euclid: 18 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35D10 35G20: Nonlinear higher-order equations 35K65: Degenerate parabolic equations


Bögelein, Verena. Very weak solutions of higher-order degenerate parabolic systems. Adv. Differential Equations 14 (2009), no. 1/2, 121--200.

Export citation