Forward, backward and elliptic Harnack inequalities for non-negative solutions to certain singular parabolic partial differential equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 2, p. 385-422
Forward, backward and elliptic Harnack inequalities for non-negative solutions of a class of singular, quasi-linear, parabolic equations, are established. These classes of singular equations include the p-Laplacean equation and equations of the porous medium type. Key novel points include form of a Harnack estimate backward in time, that has never been observed before, and measure theoretical proofs, as opposed to comparison principles. These Harnack estimates are established in the super-critical range (1.5) below. Such a range is optimal for a Harnack estimate to hold.
Classification:  35K65,  35B65,  35B45
@article{ASNSP_2010_5_9_2_385_0,
     author = {DiBenedetto, Emmanuele and Gianazza, Ugo and Vespri, Vincenzo},
     title = {Forward, backward and elliptic Harnack inequalities for non-negative solutions to certain singular parabolic partial differential equations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 9},
     number = {2},
     year = {2010},
     pages = {385-422},
     zbl = {1206.35053},
     mrnumber = {2731161},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2010_5_9_2_385_0}
}
DiBenedetto, Emmanuele; Gianazza, Ugo; Vespri, Vincenzo. Forward, backward and elliptic Harnack inequalities for non-negative solutions to certain singular parabolic partial differential equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 2, pp. 385-422. http://www.numdam.org/item/ASNSP_2010_5_9_2_385_0/

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