Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term
Dall'Aglio, A. ; Giachetti, D. ; Leone, C. ; Segura de León, S.
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006), p. 97-126 / Harvested from Numdam
@article{AIHPC_2006__23_1_97_0,
     author = {Dall'Aglio, A. and Giachetti, D. and Leone, Chiara and Segura de Le\'on, S.},
     title = {Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {23},
     year = {2006},
     pages = {97-126},
     doi = {10.1016/j.anihpc.2005.02.006},
     mrnumber = {2194583},
     zbl = {1103.35040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2006__23_1_97_0}
}
Dall'Aglio, A.; Giachetti, D.; Leone, C.; Segura de León, S. Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) pp. 97-126. doi : 10.1016/j.anihpc.2005.02.006. http://gdmltest.u-ga.fr/item/AIHPC_2006__23_1_97_0/

[1] Alt H.W., Luckhaus S., Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983) 311-341. | MR 706391 | Zbl 0497.35049

[2] Andreu F., Mazón J.M., Segura De León S., Toledo J., Existence and uniqueness for a degenerate parabolic equation with L 1 data, Trans. Amer. Math. Soc. 351 (1999) 285-306. | MR 1433108 | Zbl 0912.35092

[3] Aronson D.G., Serrin J., Local behavior of solutions of quasilinear parabolic equations, Arch. Rational Mech. Anal. 25 (1967) 81-122. | MR 244638 | Zbl 0154.12001

[4] Aubin J.P., Un théorème de compacité, C. R. Acad. Sci. 256 (1963) 5042-5044. | MR 152860 | Zbl 0195.13002

[5] Bénilan P., Boccardo L., Gallouët T., Gariepy R., Pierre M., Vázquez J.L., An L 1 theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa 22 (2) (1995) 240-273. | Numdam | MR 1354907 | Zbl 0866.35037

[6] Blanchard D., Porretta A., Nonlinear parabolic equations with natural growth terms and measure initial data, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 30 (4) (2001) 583-622. | Numdam | MR 1896079 | Zbl 1072.35089

[7] Boccardo L., Murat F., Puel J.P., Résultats d'existence pour certains problèmes elliptiques quasilinéaires, Ann. Scuola Norm. Sup. Pisa 11 (1984) 213-235. | Numdam | MR 764943 | Zbl 0557.35051

[8] Boccardo L., Murat F., Puel J.P., Existence results for some quasilinear parabolic equations, Nonlinear Anal. 13 (1989) 373-392. | MR 987375 | Zbl 0705.35066

[9] Boccardo L., Porzio M.M., Bounded solutions for a class of quasi-linear parabolic problems with a quadratic gradient term, Progr. Nonlinear Differential Equations 50 (2002) 39-48. | MR 1944156 | Zbl 1028.35058

[10] Boccardo L., Segura De León S., Trombetti C., Bounded and unbounded solutions for a class of quasi-linear elliptic problems with a quadratic grandient term, J. Math. Pures Appl. 80 (9) (2001) 919-940. | MR 1865381 | Zbl 01770851

[11] Brezis H., Analyse fonctionnelle. Théorie et applications, Collection Mathématiques Appliquées pour la Maîtrise, Masson, Paris, 1983. | MR 697382 | Zbl 0511.46001

[12] Dall'Aglio A., Giachetti D., Puel J.P., Nonlinear elliptic equations with natural growth in general domains, Ann. Mat. Pura Appl. 181 (2002) 407-426. | MR 1939689 | Zbl 1097.35050

[13] A. Dall'Aglio, D. Giachetti, J.P. Puel, Nonlinear parabolic equations with natural growth in general domains, Bull. Un. Mat. Ital., in press. | Zbl 05147142

[14] Dall'Aglio A., Orsina L., Nonlinear parabolic equations with natural growth conditions and L 1 data, Nonlinear Anal. 27 (1996) 59-73. | MR 1390712 | Zbl 0861.35045

[15] Dibenedetto E., Degenerate Parabolic Equations, Springer-Verlag, New York, 1993. | MR 1230384 | Zbl 0794.35090

[16] Evans L.C., Partial Differential Equations, Graduate Stud. in Math., vol. 19, American Mathematical Society, Providence, RI, 1998. | Zbl 0902.35002

[17] Ferone V., Murat F., Nonlinear problems having natural growth in the gradient: an existence result when the source terms are small, Nonlinear Anal. 42 (2000) 1309-1326. | MR 1780731 | Zbl 01529452

[18] Ferone V., Posteraro M.R., Rakotoson J.M., L 1 -estimates for nonlinear elliptic problems with p-growth in the gradient, J. Ineq. Appl. 3 (1999) 109-125. | MR 1733106 | Zbl 0928.35060

[19] Ferone V., Posteraro M.R., Rakotoson J.M., Nonlinear parabolic equations with p-growth and unbounded data, C. R. Acad. Sci. Paris Sèr. I Math. 328 (1999) 291-296. | MR 1675940 | Zbl 0922.35075

[20] Ferone V., Posteraro M.R., Rakotoson J.M., Nonlinear parabolic problems with critical growth and unbounded data, Indiana Univ. Math. J. 50 (3) (2001) 1201-1215. | MR 1871353 | Zbl 01780897

[21] Ladyzenskaja O.A., Solonnikov V.A., Ural'Ceva N.N., Linear and Quasi-Linear Equations of Parabolic Type, Transl. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, RI, 1968. | MR 241821 | Zbl 0174.15403

[22] Landes R., On the existence of weak solutions for quasilinear parabolic boundary value problems, Proc. Roy. Soc. Edinburgh Sect. A 89 (1981) 217-237. | MR 635759 | Zbl 0493.35054

[23] Landes R., Mustonen V., On parabolic initial-boundary value problems with critical growth for the gradient, Ann. Inst. H. Poincaré Anal. Non Linéaire 11 (1994) 135-158. | Numdam | MR 1267364 | Zbl 0836.35078

[24] Mokrane A., Existence of bounded solutions of some nonlinear parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A 107 (3-4) (1987) 313-326. | MR 924524 | Zbl 0649.35044

[25] Orsina L., Porzio M.M., L Q-estimate and existence of solutions for some nonlinear parabolic equations, Boll. Un. Math. Ital. B 6 (1992) 631-647. | MR 1191957 | Zbl 0783.35026

[26] Porretta A., Regularity for entropy solutions of a class of parabolic equations with non regular initial datum, Dynamic Systems Appl. 7 (1998) 53-71. | MR 1612029 | Zbl 0899.35049

[27] A. Porretta, S. Segura de León, Nonlinear elliptic equations having a gradient term with natural growth, Preprint.

[28] Prignet A., Existence and uniqueness of entropy solution of parabolic problems with L 1 data, Nonlinear Anal. 28 (12) (1997) 1943-1954. | MR 1436364 | Zbl 0909.35075

[29] Simon J., Compact sets in the space L p (0,T;B), Ann. Mat. Pura Appl. 146 (1987) 65-96. | MR 916688 | Zbl 0629.46031