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 Cet article a éte moissonné depuis la source American Mathematical Society

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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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     title = {Intrinsic {Harnack} estimates for nonnegative local solutions of degenerate parabolic equations},
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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

[1] Aronson, D. G., Serrin, James Local behavior of solutions of quasilinear parabolic equations Arch. Rational Mech. Anal. 1967 81 122

[2] Dibenedetto, E. Harnack estimates in certain function classes Atti Sem. Mat. Fis. Univ. Modena 1989 173 182

[3] Dibenedetto, Emmanuele Degenerate parabolic equations 1993

[4] Hadamard, J. Extension à l’équation de la chaleur d’un théorème de A. Harnack Rend. Circ. Mat. Palermo (2) 1954

[5] Ladyženskaja, O. A., Solonnikov, V. A., Ural′Ceva, N. N. Lineĭ nye i kvazilineĭ nye uravneniya parabolicheskogo tipa 1967 736

[6] Pini, Bruno Sulla soluzione generalizzata di Wiener per il primo problema di valori al contorno nel caso parabolico Rend. Sem. Mat. Univ. Padova 1954 422 434

[7] Moser, Jürgen A Harnack inequality for parabolic differential equations Comm. Pure Appl. Math. 1964 101 134

[8] Trudinger, Neil S. Pointwise estimates and quasilinear parabolic equations Comm. Pure Appl. Math. 1968 205 226

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