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In this work we prove both local and global Harnack estimates for weak supersolutions to second order nonlinear degenerate parabolic partial differential equations in divergence form. We reduce the proof to an analysis of so-called hot and cold alternatives, and use the expansion of positivity together with a parabolic type of covering argument. Our proof uses only the properties of weak supersolutions. In particular, no comparison to weak solutions is needed.
@article{ASNSP_2008_5_7_4_673_0,
author = {Kuusi, Tuomo},
title = {Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {673--716},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 7},
number = {4},
year = {2008},
mrnumber = {2483640},
zbl = {1178.35100},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_4_673_0/}
}
TY - JOUR AU - Kuusi, Tuomo TI - Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2008 SP - 673 EP - 716 VL - 7 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_4_673_0/ LA - en ID - ASNSP_2008_5_7_4_673_0 ER -
%0 Journal Article %A Kuusi, Tuomo %T Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2008 %P 673-716 %V 7 %N 4 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_4_673_0/ %G en %F ASNSP_2008_5_7_4_673_0
Kuusi, Tuomo. Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 4, pp. 673-716. http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_4_673_0/