Advances in Differential Equations

Intrinsic Harnack estimates for some doubly nonlinear degenerate parabolic equations

S. Fornaro and M. Sosio

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 prove an intrinsic Harnack inequality for non-negative local weak solutions of a wide class of doubly nonlinear degenerate parabolic equations whose prototype is \begin{equation*} u_t-\mathrm{div}(u^{m-1}|Du|^{p-2}Du)=0,\qquad p{\geqslant} 2, m{\geqslant} 1. \end{equation*} As a consequence, we get that such solutions are locally Hölder continuous.

Article information

Adv. Differential Equations, Volume 13, Number 1-2 (2008), 139-168.

First available in Project Euclid: 18 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K59: Quasilinear parabolic equations
Secondary: 35B45: A priori estimates 35B65: Smoothness and regularity of solutions 35K65: Degenerate parabolic equations 35K92: Quasilinear parabolic equations with p-Laplacian


Fornaro, S.; Sosio, M. Intrinsic Harnack estimates for some doubly nonlinear degenerate parabolic equations. Adv. Differential Equations 13 (2008), no. 1-2, 139--168.

Export citation