Geodesic
Intrinsic Harnack estimates for nonnegative local solutions of degenerate parabolic equations
DiBenedetto, Emmanuele1 ; Gianazza, Ugo2 ; Vespri, Vincenzo3
1 Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA
2 Dipartimento di Matematica “F. Casorati", Università di Pavia, via Ferrata 1, 27100 Pavia, Italy
3 Dipartimento di Matematica “U. Dini", Università di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy
Electronic research announcements of the American Mathematical Society, Tome 12 (2006), pp. 95-99.

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S1079-6762-06-00166-1

DiBenedetto, Emmanuele 1 ; Gianazza, Ugo 2 ; Vespri, Vincenzo 3

1 Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA
2 Dipartimento di Matematica “F. Casorati", Università di Pavia, via Ferrata 1, 27100 Pavia, Italy
3 Dipartimento di Matematica “U. Dini", Università di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy 
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DiBenedetto, Emmanuele; Gianazza, Ugo; Vespri, Vincenzo. Intrinsic Harnack estimates for nonnegative local solutions of degenerate parabolic equations. Electronic research announcements of the American Mathematical Society, Tome 12 (2006), pp. 95-99. doi : 10.1090/S1079-6762-06-00166-1. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-06-00166-1/

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