Geodesic
Singular Dirichlet Problems with Quadratic Gradient
Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 3, pp. 559-574.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We study the existence of solution for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradient. 
@article{BUMI_2009_9_2_3_a1,
     author = {Mart{\'\i}nez-Aparicio, Pedro J.},
     title = {Singular {Dirichlet} {Problems} with {Quadratic} {Gradient}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {559--574},
     publisher = {mathdoc},
     volume = {Ser. 9, 2},
     number = {3},
     year = {2009},
     zbl = {1206.35132},
     mrnumber = {2569290},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_3_a1/}
}
TY  - JOUR
AU  - Martínez-Aparicio, Pedro J.
TI  - Singular Dirichlet Problems with Quadratic Gradient
JO  - Bollettino della Unione matematica italiana
PY  - 2009
SP  - 559
EP  - 574
VL  - 2
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_3_a1/
LA  - en
ID  - BUMI_2009_9_2_3_a1
ER  - 
%0 Journal Article
%A Martínez-Aparicio, Pedro J.
%T Singular Dirichlet Problems with Quadratic Gradient
%J Bollettino della Unione matematica italiana
%D 2009
%P 559-574
%V 2
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_3_a1/
%G en
%F BUMI_2009_9_2_3_a1
Martínez-Aparicio, Pedro J. Singular Dirichlet Problems with Quadratic Gradient. Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 3, pp. 559-574. http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_3_a1/

[1] D. Arcoya - S. Barile - P. J. Martínez-Aparicio, Singular quasilinear equations with quadratic growth in the gradient without sign condition. J. Math. Anal. Appl., 350 (2009), 401-408. | DOI | MR | Zbl

[2] D. Arcoya - P. J. Martínez-Aparicio, Quasilinear equations with natural growth, Rev. Mat. Iberoam., 24 (2008), 597-616. | fulltext EuDML | DOI | MR | Zbl

[3] D. Arcoya - S. Segura De Leon, Uniqueness of solutions for some elliptic equations with a quadratic gradient term. ESAIM: Control, Optimization and the Calculus of Variations, (2008) DOI:10.1051/cocv:2008072. | fulltext EuDML | DOI | MR

[4] L. Boccardo, Dirichlet problems with singular and quadratic gradient lower order terms, ESAIM: Control, Optimization and the Calculus of Variations, 14 (2008) 411-426. | fulltext EuDML | DOI | MR | Zbl

[5] L. Boccardo - T. Gallouët, Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal., 87 (1989), 149-169. | DOI | MR

[6] L. Boccardo - T. Gallouët, Strongly nonlinear elliptic equations having natural growth terms and $L^{1}$ data, Nonlinear Anal. 19 (1992), 573-579. | DOI | MR | Zbl

[7] L. Boccardo - T. Gallouët - F. Murat, A unified presentation of two existence results for problems with natural growth, Progress in partial differential equations: the Metz surveys, 2 (1992), 127-137, Pitman Res. Notes Math. Ser., 296, Longman Sci. Tech., Harlow, 1993. | MR

[8] L. Boccardo - F. Murat - J-P. Puel, Existence de solutions non bornées pour certaines equations quasi-lineaires, Portugal. Math. 41 (1982), 507-534. | fulltext EuDML | MR | Zbl

[9] M. G. Crandall - P. H. Rabinowitz - L. Tartar, On a Dirichlet problem with a singular nonlinearity, Comm. Partial Differential Equations 2 (1977), 193-222. | DOI | MR | Zbl

[10] D. Giachetti - F. Murat, An elliptic problem with a lower order term having singular behaviour, Boll. Un. Mat. Ital. B, (9), II (2009). | MR | Zbl

[11] D. Gilbarg - N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983. | DOI | MR | Zbl

[12] O. Ladyzenskaya - N. Uralt'Seva, Linear and quasilinear elliptic equations; Translated by Scripta Technica. New York, Academic Press, 1968. | MR

[13] A. C. Lazer - P. J. Mckenna, On a singular nonlinear elliptic boundary-value problem, Proc. Amer. Math. Soc., 111 (1991), 721-730. | DOI | MR | Zbl

[14] J. Leray - J. L. Lions, Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder, Bull. Soc. Math. France, 93 (1965), 97-107. | fulltext EuDML | MR | Zbl

[15] G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble), 15 (1965), 189-258. | fulltext EuDML | MR | Zbl