Summability of semicontinuous supersolutions to a quasilinear parabolic equation

Kinnunen, Juha; Lindqvist, Peter

Kinnunen, Juha ; Lindqvist, Peter

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 1, pp. 59-78.

Résumé

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.

MR 2165403 | Zbl 1107.35070 | 1 citation dans Numdam

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},
     pages = {59--78},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 4},
     number = {1},
     year = {2005},
     zbl = {1107.35070},
     mrnumber = {2165403},
     language = {en},
     url = {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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