On a Liouville comparison principle for entire weak solutions of quasilinear elliptic partial differential inequalities

Kurta, Vasilii V.

doi:10.1016/j.crma.2004.06.025

Partial Differential Equations/Potential Theory

On a Liouville comparison principle for entire weak solutions of quasilinear elliptic partial differential inequalities
[Sur un principe de comparaison de type Liouville pour des solutions entières faibles d'inégalités aux dérivées partielles elliptiques quasi linéaires.]

Présenté par : Pierre-Louis Lions

Kurta, Vasilii V.¹

¹ Mathematical Reviews, 416 Fourth Street, P.O. Box 8604, Ann Arbor, Michigan 48107-8604, USA

Comptes Rendus. Mathématique, Tome 339 (2004) no. 6, pp. 401-404

Abstract (VO)
Résumé

We establish a new Liouville-type comparison principle for entire weak solutions of quasilinear elliptic partial differential inequalities of the form $A (u) ⩽ A (v)$ on $R^{n}$ , $n ⩾ 2$ . Typical examples of the operator $A (w)$ are the p-Laplacian and its well-known modifications for $1 < p ⩽ 2$ .

On établit un nouveau principe de comparaison de type Liouville pour des solutions entières faibles d'inégalités aux dérivées partielles elliptiques quasi linéaires de la forme $A (u) ⩽ A (v)$ dans $R^{n}$ , $n ⩾ 2$ . Le p-laplacien et ses modifications bien connues pour $1 < p ⩽ 2$ sont des exemples typiques de l'opérateur $A (w)$ .

Reçu le : 2004-03-03
Accepté le : 2004-06-29
Publié le : 2004-08-21

DOI : 10.1016/j.crma.2004.06.025

Affiliations des auteurs :

Kurta, Vasilii V. ¹

¹ Mathematical Reviews, 416 Fourth Street, P.O. Box 8604, Ann Arbor, Michigan 48107-8604, USA

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     title = {On a {Liouville} comparison principle for entire weak solutions of quasilinear elliptic partial differential inequalities},
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     pages = {401--404},
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Kurta, Vasilii V. On a Liouville comparison principle for entire weak solutions of quasilinear elliptic partial differential inequalities. Comptes Rendus. Mathématique, Tome 339 (2004) no. 6, pp. 401-404. doi: 10.1016/j.crma.2004.06.025

Bibliographie
Cité par

[1] V.V. Kurta, Some problems of qualitative theory for nonlinear second-order equations, Doctoral Dissert., Steklov Math. Inst., Moscow, 1994

[2] Kurta, V.V. Comparison principle for solutions of parabolic inequalities, C. R. Acad. Sci. Paris, Ser. I, Volume 322 (1996), pp. 1175-1180

[3] Kurta, V.V. About a Liouville phenomenon, C. R. Acad. Sci. Paris, Ser. I, Volume 338 (2004), pp. 19-22

[4] Lions, J.-L. Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars, Paris, 1969

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