Liouville Theorems for Some Nonlinear Inequalities
Informatics and Automation, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 97-118.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove various Liouville theorems for integral and differential inequalities on the whole $\mathbb R^N$. The main tools we use throughout this paper are representation formulae for linear inequalities, the nonlinear capacity method and the weak form of Harnack's inequality.
@article{TRSPY_2008_260_a6,
     author = {G. Caristi and L. D'Ambrosio and E. Mitidieri},
     title = {Liouville {Theorems} for {Some} {Nonlinear} {Inequalities}},
     journal = {Informatics and Automation},
     pages = {97--118},
     publisher = {mathdoc},
     volume = {260},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a6/}
}
TY  - JOUR
AU  - G. Caristi
AU  - L. D'Ambrosio
AU  - E. Mitidieri
TI  - Liouville Theorems for Some Nonlinear Inequalities
JO  - Informatics and Automation
PY  - 2008
SP  - 97
EP  - 118
VL  - 260
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a6/
LA  - en
ID  - TRSPY_2008_260_a6
ER  - 
%0 Journal Article
%A G. Caristi
%A L. D'Ambrosio
%A E. Mitidieri
%T Liouville Theorems for Some Nonlinear Inequalities
%J Informatics and Automation
%D 2008
%P 97-118
%V 260
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a6/
%G en
%F TRSPY_2008_260_a6
G. Caristi; L. D'Ambrosio; E. Mitidieri. Liouville Theorems for Some Nonlinear Inequalities. Informatics and Automation, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 97-118. http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a6/

[1] Bidaut-Véron M. F., Pohozaev S. I., “Nonexistence results and estimates for some nonlinear elliptic problems”, J. Anal. Math., 84 (2001), 1–49 | DOI | MR | Zbl

[2] Caristi G., D'Ambrosio L., Mitidieri E., Liouville theorems and representation formulae for higher order problems and systems, Preprint, 2007

[3] D'Ambrosio L., Mitidieri E., Pohozaev S. I., “Representation formulae and inequalities for solutions of a class of second order partial differential equations”, Trans. Amer. Math. Soc., 358:2 (2006), 893–910 | DOI | MR

[4] Heinonen J., Lectures on analysis on metric spaces, Universitext, Springer–Verlag, New York, 2001 | MR

[5] Li Y. Y., “Remark on some conformally invariant integral equations: the method of moving spheres”, J. Eur. Math. Soc., 6:2 (2004), 153–180 | MR

[6] Lieb E. H., Loss M., Analysis, Grad. Stud. Math., 14, Amer. Math. Soc., Providence, RI, 2001 | MR | Zbl

[7] Malý J., Ziemer W. P., Fine regularity of solutions of elliptic partial differential equations, Math. Surv. and Monogr., 51, Amer. Math. Soc., Providence, RI, 1997 | MR | Zbl

[8] Mitidieri E., Pokhozhaev S. I., Apriornye otsenki i otsutstvie reshenii nelineinykh uravnenii i neravenstv v chastnykh proizvodnykh, Tr. MIAN, 234, Nauka, M., 2001 | MR

[9] Mitidieri E., Pokhozhaev S. I., “Svoistvo polozhitelnosti reshenii nekotorykh nelineinykh ellipticheskikh neravenstv v $\mathbb R^n$”, DAN, 393:2 (2003), 159–164 | MR

[10] Mitidieri E., Pokhozhaev S. I., “Liuvillevy teoremy dlya nekotorykh klassov nelineinykh nelokalnykh zadach”, Tr. MIAN, 248, Nauka, M., 2005, 164–184 | MR

[11] Serrin J., Zou H., “Cauchy–Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities”, Acta math., 189 (2002), 79–142 | DOI | MR | Zbl

[12] Stein E. M., Harmonic analysis: Real-variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, 1993 | MR | Zbl

[13] Stroock D. W., Probability theory: An analytic view, Cambridge Univ. Press, Cambridge, 1993 | MR | Zbl

[14] Torchinsky A., Real-variable methods in harmonic analysis, Acad. Press, Orlando, 1986 | MR | Zbl