Geodesic
Summability of semicontinuous supersolutions to a quasilinear parabolic equation
Kinnunen, Juha1 ; Lindqvist, Peter2 
1 Department of Mathematical Sciences University of Oulu P.O. Box 3000 FI-90014 Oulu, Finland
2 Department of Mathematics Norwegian University of Science and Technology N-7491 Trondheim, Norway
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 1, pp. 59-78

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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

Kinnunen, Juha 1 ; Lindqvist, Peter 2

1 Department of Mathematical Sciences University of Oulu P.O. Box 3000 FI-90014 Oulu, Finland
2 Department of Mathematics Norwegian University of Science and Technology N-7491 Trondheim, Norway 
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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://geodesic.mathdoc.fr/item/ASNSP_2005_5_4_1_59_0/