Comptes Rendus
Partial Differential Equations/Potential Theory
On a Liouville comparison principle for entire weak solutions of quasilinear elliptic partial differential inequalities
Comptes Rendus. Mathématique, Volume 339 (2004) no. 6, pp. 401-404.

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 Rn, n2. Typical examples of the operator A(w) are the p-Laplacian and its well-known modifications for 1<p2.

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 Rn, n2. Le p-laplacien et ses modifications bien connues pour 1<p2 sont des exemples typiques de l'opérateur A(w).

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.06.025
Vasilii V. Kurta 1

1 Mathematical Reviews, 416 Fourth Street, P.O. Box 8604, Ann Arbor, Michigan 48107-8604, USA
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     author = {Vasilii V. Kurta},
     title = {On a {Liouville} comparison principle for entire weak solutions of quasilinear elliptic partial differential inequalities},
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Vasilii V. Kurta. On a Liouville comparison principle for entire weak solutions of quasilinear elliptic partial differential inequalities. Comptes Rendus. Mathématique, Volume 339 (2004) no. 6, pp. 401-404. doi : 10.1016/j.crma.2004.06.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.06.025/

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

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

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

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

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