[Sur un principe de comparaison de type Liouville pour des solutions d'inégalités elliptiques quasi-linéaires]
On caractérise en terme de monotonie, des propriétés fondamentales d'opérateurs aux dérivées partielles, elliptiques, quasi-linéaires permettant d'établir un principe de comparaison de type Liouville, des solutions faibles d'inégalités aux dérivée partielles, elliptiques, quasi-linéaires de la forme A(u)+|u|q−1u⩽A(v)+|v|q−1v. Ces solutions appartiennent seulement localement aux espaces de Sobolev correspondant dans . On montre que ces propriétés sont valables pour une large classe d'opérateurs aux dérivées partielles elliptiques, quasi-linéaires. Des exemples typiques de tels opérateurs sont le p-laplacien et ses modifications bien connues pour 1<p⩽2.
We characterize in terms of monotonicity basic properties of quasilinear elliptic partial differential operators which make it possible to obtain a Liouville-type comparison principle for entire solutions of quasilinear elliptic partial differential inequalities of the form A(u)+|u|q−1u⩽A(v)+|v|q−1v, which belong only locally to the corresponding Sobolev spaces on . We establish that such properties are inherent for a wide class of quasilinear elliptic partial differential operators. Typical examples of such operators are the p-Laplacian and its well-known modifications for 1<p⩽2.
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@article{CRMATH_2003__336_11_897_0,
author = {Kurta, Vasilii V.},
title = {On a {Liouville-type} comparison principle for solutions of~quasilinear elliptic inequalities},
journal = {Comptes Rendus. Math\'ematique},
pages = {897--900},
publisher = {Elsevier},
volume = {336},
number = {11},
year = {2003},
doi = {10.1016/S1631-073X(03)00225-5},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00225-5/}
}
TY - JOUR AU - Kurta, Vasilii V. TI - On a Liouville-type comparison principle for solutions of quasilinear elliptic inequalities JO - Comptes Rendus. Mathématique PY - 2003 SP - 897 EP - 900 VL - 336 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(03)00225-5/ DO - 10.1016/S1631-073X(03)00225-5 LA - en ID - CRMATH_2003__336_11_897_0 ER -
%0 Journal Article %A Kurta, Vasilii V. %T On a Liouville-type comparison principle for solutions of quasilinear elliptic inequalities %J Comptes Rendus. Mathématique %D 2003 %P 897-900 %V 336 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(03)00225-5/ %R 10.1016/S1631-073X(03)00225-5 %G en %F CRMATH_2003__336_11_897_0
Kurta, Vasilii V. On a Liouville-type comparison principle for solutions of quasilinear elliptic inequalities. Comptes Rendus. Mathématique, Tome 336 (2003) no. 11, pp. 897-900. doi : 10.1016/S1631-073X(03)00225-5. http://www.numdam.org/articles/10.1016/S1631-073X(03)00225-5/
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☆ This work was reported by the author at the 981st AMS Meeting in October, 2002.
