Geodesic
On some partial differential inequalities with gradient terms
Informatics and Automation, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 40-48.

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

Using a modification of the nonlinear capacity method, we obtain necessary conditions for the solvability of some nonlinear partial differential equations and inequalities containing the polyharmonic operator and terms that depend on the norm of the gradient of the solution, both in the entire space and in bounded domains; in the latter case the coefficients of the inequality are allowed to have singularities. 
@article{TRSPY_2013_283_a3,
     author = {E. I. Galakhov},
     title = {On some partial differential inequalities with gradient terms},
     journal = {Informatics and Automation},
     pages = {40--48},
     publisher = {mathdoc},
     volume = {283},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2013_283_a3/}
}
TY  - JOUR
AU  - E. I. Galakhov
TI  - On some partial differential inequalities with gradient terms
JO  - Informatics and Automation
PY  - 2013
SP  - 40
EP  - 48
VL  - 283
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2013_283_a3/
LA  - ru
ID  - TRSPY_2013_283_a3
ER  - 
%0 Journal Article
%A E. I. Galakhov
%T On some partial differential inequalities with gradient terms
%J Informatics and Automation
%D 2013
%P 40-48
%V 283
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2013_283_a3/
%G ru
%F TRSPY_2013_283_a3
E. I. Galakhov. On some partial differential inequalities with gradient terms. Informatics and Automation, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 40-48. http://geodesic.mathdoc.fr/item/TRSPY_2013_283_a3/

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

[2] Pokhozhaev S.I., “Suschestvenno nelineinye emkosti, porozhdennye differentsialnymi operatorami”, DAN, 357:5 (1997), 592–594 | MR | Zbl

[3] Pokhozhaev S.I., “Ob otsutstvii globalnykh reshenii uravneniya Gamiltona–Yakobi”, Dif. uravneniya, 44:10 (2008), 1405–1415 | MR

[4] Pokhozhaev S.I., “O globalnoi razreshimosti uravneniya Kuramoto–Sivashinskogo pri ogranichennykh nachalnykh dannykh”, Mat. sb., 200:7 (2009), 131–144 | DOI | MR | Zbl

[5] D'Ambrosio L., Mitidieri E., “A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities”, Adv. Math., 224 (2010), 967–1020 | DOI | MR | Zbl

[6] Farina A., Serrin J., “Entire solutions of completely coercive quasilinear elliptic equations”, J. Diff. Eqns., 250 (2011), 4367–4408 | DOI | MR | Zbl

[7] Farina A., Serrin J., “Entire solutions of completely coercive quasilinear elliptic equations. II”, J. Diff. Eqns., 250 (2011), 4409–4436 | DOI | MR | Zbl

[8] Filippucci R., “Nonexistence of positive weak solutions of elliptic inequalities”, Nonlinear Anal., Theory Methods Appl., 70 (2009), 2903–2916 | DOI | MR | Zbl

[9] Filippucci R., Pucci P., Rigoli M., “Nonlinear weighted $p$-Laplacian elliptic inequalities with gradient terms”, Commun. Contemp. Math., 12 (2010), 501–535 | DOI | MR | Zbl

[10] Li X., Li F., “Nonexistence of solutions for singular quasilinear differential inequalities with a gradient nonlinearity”, Nonlinear Anal., Theory Methods Appl., 75 (2012), 2812–2822 | DOI | MR | Zbl

[11] Pucci P., Serrin J., “A remark on entire solutions of quasilinear elliptic equations”, J. Diff. Eqns., 250 (2011), 675–689 | DOI | MR | Zbl

[12] Serrin J., “Entire solutions of quasilinear elliptic equations”, J. Math. Anal. Appl., 352 (2009), 3–14 | DOI | MR | Zbl