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Intrinsic Harnack estimates for nonnegative local solutions of degenerate parabolic equations

Author(s): Emmanuele DiBenedetto; Ugo Gianazza; Vincenzo Vespri
Journal: Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 95-99.
MSC (2000): Primary 35K65, 35B65; Secondary 35B45
Posted: August 2, 2006
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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
Email: em.diben@vanderbilt.edu

Ugo Gianazza
Affiliation: Dipartimento di Matematica ``F. Casorati", Università di Pavia, via Ferrata 1, 27100 Pavia, Italy
Email: gianazza@imati.cnr.it

Vincenzo Vespri
Affiliation: Dipartimento di Matematica ``U. Dini", Università di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy
Email: vespri@math.unifi.it

DOI: 10.1090/S1079-6762-06-00166-1
PII: S 1079-6762(06)00166-1
Keywords: Degenerate parabolic equations, Harnack estimates, H\"older continuity
Received by editor(s): January 20, 2006
Posted: August 2, 2006
Communicated by: Luis A. Caffarelli
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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