Summability of semicontinuous supersolutions to a quasilinear parabolic equation

Juha Kinnunen[1]; Peter Lindqvist[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

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2005)

  • Volume: 4, Issue: 1, page 59-78
  • ISSN: 0391-173X

Abstract

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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.

How to cite

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Kinnunen, Juha, and Lindqvist, Peter. "Summability of semicontinuous supersolutions to a quasilinear parabolic equation." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 4.1 (2005): 59-78. <http://eudml.org/doc/84556>.

@article{Kinnunen2005,
abstract = {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.},
affiliation = {Department of Mathematical Sciences University of Oulu P.O. Box 3000 FI-90014 Oulu, Finland; Department of Mathematics Norwegian University of Science and Technology N-7491 Trondheim, Norway},
author = {Kinnunen, Juha, Lindqvist, Peter},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Sobolev derivative; -superparabolic functions},
language = {eng},
number = {1},
pages = {59-78},
publisher = {Scuola Normale Superiore, Pisa},
title = {Summability of semicontinuous supersolutions to a quasilinear parabolic equation},
url = {http://eudml.org/doc/84556},
volume = {4},
year = {2005},
}

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
PB - Scuola Normale Superiore, Pisa
VL - 4
IS - 1
SP - 59
EP - 78
AB - 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.
LA - eng
KW - Sobolev derivative; -superparabolic functions
UR - http://eudml.org/doc/84556
ER -

References

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  10. [10] P. Lindqvist, On the definition and properties of p -superharmonic functions, J. Reine Angew. Math. 365 (1986), 67–79. Zbl0572.31004MR826152
  11. [11] G. Lieberman, “Second Order Parabolic Equations”, World Scientific, Singapore, 1996. Zbl0884.35001MR1465184
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  13. [13] J. Moser, Correction to: “A Harnack inequality for parabolic differential equations”, Comm. Pure Appl. Math. 20 (1967), 231–236. Zbl0149.07001MR203268
  14. [14] N. Trudinger, Pointwise estimates and quasilinear parabolic equations, Comm. Pure Appl. Math. 21 (1968), 205–226. Zbl0159.39303MR226168
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