Dans cet article nous utilisons les propriétés des fonctions avec puissance radiale afin d'obtenir des contre-exemples à certaines inéquations de type Caccioppoli et Harnack faible pour les fonctions quasisuperharmoniques, lesquelles sont bien connues être valables pour les fonctions p-superharmoniques. Nous obtenons aussi de nouvelles bornes pour l'intégrabilité locale des fonctions quasisuperharmoniques. De plus nous démontrons que le logarithme d'une fonction positive quasiminimisante est de type BMO, et appartient à un espace de Sobolev.
In this paper we use quasiminimizing properties of radial power-type functions to deduce counterexamples to certain Caccioppoli-type inequalities and weak Harnack inequalities for quasisuperharmonic functions, both of which are well known to hold for p-superharmonic functions. We also obtain new bounds on the local integrability for quasisuperharmonic functions. Furthermore, we show that the logarithm of a positive quasisuperminimizer has bounded mean oscillation and belongs to a Sobolev type space.
@article{AIHPC_2010__27_6_1489_0,
author = {Bj\"orn, Anders and Bj\"orn, Jana and Marola, Niko},
title = {BMO, integrability, Harnack and Caccioppoli inequalities for quasiminimizers},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {27},
year = {2010},
pages = {1489-1505},
doi = {10.1016/j.anihpc.2010.09.005},
mrnumber = {2738330},
zbl = {1219.49003},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_2010__27_6_1489_0}
}
Björn, Anders; Björn, Jana; Marola, Niko. BMO, integrability, Harnack and Caccioppoli inequalities for quasiminimizers. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) pp. 1489-1505. doi : 10.1016/j.anihpc.2010.09.005. http://gdmltest.u-ga.fr/item/AIHPC_2010__27_6_1489_0/
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