Advances in Differential Equations

Intrinsic Harnack estimates for some doubly nonlinear degenerate parabolic equations

S. Fornaro and M. Sosio

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Abstract

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

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

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867362

Mathematical Reviews number (MathSciNet)
MR2482539

Zentralblatt MATH identifier
1160.35039

Subjects
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

Citation

Fornaro, S.; Sosio, M. Intrinsic Harnack estimates for some doubly nonlinear degenerate parabolic equations. Adv. Differential Equations 13 (2008), no. 1-2, 139--168. https://projecteuclid.org/euclid.ade/1355867362.


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