On a Liouville phenomenon for entire weak supersolutions of elliptic partial differential equations
Kurta, Vasilii V.
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006), p. 839-848 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2006__23_6_839_0,
     author = {Kurta, Vasilii V.},
     title = {On a Liouville phenomenon for entire weak supersolutions of elliptic partial differential equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {23},
     year = {2006},
     pages = {839-848},
     doi = {10.1016/j.anihpc.2005.12.001},
     mrnumber = {2271696},
     zbl = {05138721},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2006__23_6_839_0}
}

Kurta, Vasilii V. On a Liouville phenomenon for entire weak supersolutions of elliptic partial differential equations. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) pp. 839-848. doi : 10.1016/j.anihpc.2005.12.001. http://gdmltest.u-ga.fr/item/AIHPC_2006__23_6_839_0/

[1] Gilbarg D., Serrin J., On isolated singularities of solutions of second order elliptic differential equations, J. Analyse Math. 4 (1955/56) 309-340. | MR 81416 | Zbl 0071.09701

[2] Hayman W.K., Kennedy P.B., Subharmonic Functions, Academic Press, 1976, (284 p.). | MR 460672 | Zbl 0419.31001

[3] Heinonen J., Kilpeläinen T., Martio O., Nonlinear Potential Theory of Degenerate Elliptic Equations, Clarendon Press, 1993, (363 p.). | MR 1207810 | Zbl 0780.31001

[4] Kolmogorov A.N., Fomin S.V., Introductory Real Analysis, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1970, (403 p.). | MR 267052 | Zbl 0213.07305

[5] Kurta V.V., About a Liouville phenomenon, C. R. Math. Acad. Sci. Paris, Ser. I 338 (2004) 19-22. | MR 2038077 | Zbl 1046.35033

[6] V.V. Kurta, Some problems of qualitative theory for nonlinear second-order equations, Doctoral Dissert., Steklov Math. Inst., Moscow, 1994 (323 p.).

[7] Lichtenstein L., Beiträge zur Theorie der linearen partiellen Differentialgleichungen zweiter Ordnung vom elliptischen Typus. Unendliche Folgen positiver Lösungen, Rend. Circ. Mat. Palermo 33 (1912) 201-211. | JFM 43.0448.01

[8] Lions J.-L., Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Gauthier-Villars, Paris, 1969, (554 p.). | MR 259693 | Zbl 0189.40603

[9] Maz'Ya V.G., Shaposhnikova T.O., Theory of Multipliers in Spaces of Differentiable Functions, Pitman, Boston, MA, 1985, (Advanced Publishing Program, 344 p.). | MR 785568 | Zbl 0645.46031

[10] Miklyukov V.M., Capacity and a generalized maximum principle for quasilinear equations of elliptic type, Dokl. Akad. Nauk SSSR 250 (1980) 1318-1320. | MR 564335 | Zbl 0553.35026

[11] Miklyukov V.M., Asymptotic properties of subsolutions of quasilinear equations of elliptic type and mappings with bounded distortion, Mat. Sb. 111 (153) (1980) 42-66. | MR 560463 | Zbl 0428.35036

[12] Moser J., On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961) 577-591. | MR 159138 | Zbl 0111.09302

[13] Reshetnyak Yu.G., Mappings with bounded distortion as extremals of integrals of Dirichlet type, Sibirsk. Mat. Zh. 9 (1968) 652-666. | MR 230900 | Zbl 0162.38202

[14] Serrin J., Local behavior of solutions of quasi-linear equations, Acta Math. 111 (1964) 247-302. | MR 170096 | Zbl 0128.09101