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Intrinsic Harnack estimates for nonnegative local solutions of degenerate parabolic equations

Authors: Emmanuele DiBenedetto, Ugo Gianazza and Vincenzo Vespri
Journal: Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 95-99
MSC (2000): Primary 35K65, 35B65; Secondary 35B45
Published electronically: August 2, 2006
MathSciNet review: 2237273
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Abstract: We establish the intrinsic Harnack inequality for nonnegative solutions of the parabolic $ p$-Laplacian equation by a proof that uses neither the comparison principle nor explicit self-similar solutions. The significance is that the proof applies to quasilinear $ p$-Laplacian-type equations, thereby solving a long-standing problem in the theory of degenerate parabolic equations.

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Additional Information

Emmanuele DiBenedetto
Affiliation: Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA

Ugo Gianazza
Affiliation: Dipartimento di Matematica “F. Casorati", Università di Pavia, via Ferrata 1, 27100 Pavia, Italy

Vincenzo Vespri
Affiliation: Dipartimento di Matematica “U. Dini", Università di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy

Keywords: Degenerate parabolic equations, Harnack estimates, H\"older continuity
Received by editor(s): January 20, 2006
Published electronically: August 2, 2006
Communicated by: Luis A. Caffarelli
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.