Remarks on the maximum principle for nonlinear elliptic PDEs with quadratic growth conditions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 28 (1999) no. 3, p. 381-404 
@article{ASNSP_1999_4_28_3_381_0,
     author = {Barles, Guy and Blanc, Alain-Philippe and Georgelin, Christine and Kobylanski, Magdalena},
     title = {Remarks on the maximum principle for nonlinear elliptic PDEs with quadratic growth conditions},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 28},
     number = {3},
     year = {1999},
     pages = {381-404},
     zbl = {0940.35078},
     mrnumber = {1736522},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1999_4_28_3_381_0}
}

Barles, Guy; Blanc, Alain-Philippe; Georgelin, Christine; Kobylanski, Magdalena. Remarks on the maximum principle for nonlinear elliptic PDEs with quadratic growth conditions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 28 (1999) no. 3, pp. 381-404. http://www.numdam.org/item/ASNSP_1999_4_28_3_381_0/

[1] G. Barles - F. Murat, The Maximum Principle for quasilinear elliptic equations with quadratic growth conditions, Arch. Rational Mech. Anal. 133 (1995), 77-101. | MR 1367357 | Zbl 0859.35031

[2] A. Bensoussan - L. Boccardo - F. Murat, On a nonlinear partial differential equation having natural growth terms and unbounded solution, Ann. Inst. H. Poincaré, Anal. Non Linéaire 5 (1988), 347-364. | Numdam | MR 963104 | Zbl 0696.35042

[3] L. Boccardo - F. Murat - J.P. Puel, Existence de solutions non bornées pour certaines équations quasi-linéaires, Portugal. Math. 41 (1982), 507-534. | MR 766873 | Zbl 0524.35041

[4] L. Boccardo - F. Murat - J.-P. Puel, Existence de solutions faibles pour des équations elleptiques quasi-linéaires à croissance quadratique, In: "Nonlinear Partial Differential and their Applications", Collège de France Seminar, volume IV, H. Brezis and J.-L. Lions editors, Research Notes in Mathematics 84, Pitman, London, 1983, pp. 19-73. | MR 716511 | Zbl 0588.35041

[5] V. Ferone - F. Murat, Nonlinear problems having natural growth in the gradient: an existence result when the source term is small, Nonlinear Anal., to appear. | MR 1780731 | Zbl 1158.35358 | Zbl 01529452

[6] V. Ferone - F. Murat, Quasilinear problems having natural growth in the gradient: an existence result when the source term is small, In: "Equations aux dérivées partielles et applications, article dédié à Jacques-Louis Lions", Gauthier-Villars, Paris, 1998, pp. 497-515. | MR 1648236 | Zbl 0917.35039

[7] V. Ferone - M.R. Posteraro, On a class of quasilinear elliptic equations with quadratic growth in the gradient, Nonlinear Anal. 20 (1993). | MR 1214736 | Zbl 0801.35028

[8] D. Gilbarg - N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order", Springer-Verlag, Berlin, 1977. | MR 473443 | Zbl 0361.35003

[9] J.L. Kazdan - R.J. Kramer, Invariant criteria for existence of solutions of second order quasi-linear elliptic equations, Comm. Pure Appl. Math. 31 (1978), 619-645. | MR 477446 | Zbl 0368.35031

[10] O.A. Lady - N.N. Ural'Ceva, "Équations aux derivées partielles de type elliptique, Dunod, Paris, 1968. | MR 239273 | Zbl 0164.13001

[11] J.M. Lasry - P.L. Lions, A remark on regularization in Hilbert spaces, Isr. J. Math. 55 (1986), 257-266. | MR 876394 | Zbl 0631.49018