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, p. 59-78
We study the so-called $p$-superparabolic functions, which are defined as lower semicontinuous supersolutions of a quasilinear parabolic equation. In the linear case, when $p=2$, we have supercaloric functions and the heat equation. We show that the $p$-superparabolic functions have a spatial Sobolev gradient and a sharp summability exponent is given.
Classification:  35K55
@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},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 4},
number = {1},
year = {2005},
pages = {59-78},
zbl = {1107.35070},
mrnumber = {2165403},
language = {en},
url = {http://www.numdam.org/item/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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