We study the so-called -superparabolic functions, which are defined as lower semicontinuous supersolutions of a quasilinear parabolic equation. In the linear case, when , we have supercaloric functions and the heat equation. We show that the -superparabolic functions have a spatial Sobolev gradient and a sharp summability exponent is given.
@article{ASNSP_2005_5_4_1_59_0,
author = {Kinnunen, Juha and Lindqvist, Peter},
title = {Summability of semicontinuous supersolutions to a quasilinear parabolic equation},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {59--78},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 4},
number = {1},
year = {2005},
mrnumber = {2165403},
zbl = {1107.35070},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2005_5_4_1_59_0/}
}
TY - JOUR AU - Kinnunen, Juha AU - Lindqvist, Peter TI - Summability of semicontinuous supersolutions to a quasilinear parabolic equation JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2005 SP - 59 EP - 78 VL - 4 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2005_5_4_1_59_0/ LA - en ID - ASNSP_2005_5_4_1_59_0 ER -
%0 Journal Article %A Kinnunen, Juha %A Lindqvist, Peter %T Summability of semicontinuous supersolutions to a quasilinear parabolic equation %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2005 %P 59-78 %V 4 %N 1 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2005_5_4_1_59_0/ %G en %F ASNSP_2005_5_4_1_59_0
Kinnunen, Juha; Lindqvist, Peter. Summability of semicontinuous supersolutions to a quasilinear parabolic equation. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 1, pp. 59-78. http://www.numdam.org/item/ASNSP_2005_5_4_1_59_0/
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