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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
MathSciNet review:
2237273
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Abstract:
We establish the intrinsic Harnack inequality for nonnegative solutions of the parabolic  -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  -Laplacian-type equations, thereby solving a long-standing problem in the theory of degenerate parabolic equations.
References:
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- 2.
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- 3.
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 , Rend. Lincei Mat. Appl. 17 (2006), 223-225. - 5.
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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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