@article{AIHPC_2006__23_1_97_0, author = {Dall'Aglio, A. and Giachetti, D. and Leone, C. 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}, pages = {97--126}, publisher = {Elsevier}, volume = {23}, number = {1}, year = {2006}, doi = {10.1016/j.anihpc.2005.02.006}, mrnumber = {2194583}, zbl = {1103.35040}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2005.02.006/} }
TY - JOUR AU - Dall'Aglio, A. AU - Giachetti, D. AU - Leone, C. AU - Segura de León, S. TI - Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term JO - Annales de l'I.H.P. Analyse non linéaire PY - 2006 SP - 97 EP - 126 VL - 23 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2005.02.006/ DO - 10.1016/j.anihpc.2005.02.006 LA - en ID - AIHPC_2006__23_1_97_0 ER -
%0 Journal Article %A Dall'Aglio, A. %A Giachetti, D. %A Leone, C. %A Segura de León, S. %T Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term %J Annales de l'I.H.P. Analyse non linéaire %D 2006 %P 97-126 %V 23 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2005.02.006/ %R 10.1016/j.anihpc.2005.02.006 %G en %F 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) no. 1, pp. 97-126. doi : 10.1016/j.anihpc.2005.02.006. http://www.numdam.org/articles/10.1016/j.anihpc.2005.02.006/
[1] Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983) 311-341. | MR | Zbl
, ,[2] Existence and uniqueness for a degenerate parabolic equation with data, Trans. Amer. Math. Soc. 351 (1999) 285-306. | MR | Zbl
, , , ,[3] Local behavior of solutions of quasilinear parabolic equations, Arch. Rational Mech. Anal. 25 (1967) 81-122. | MR | Zbl
, ,[4] Un théorème de compacité, C. R. Acad. Sci. 256 (1963) 5042-5044. | MR | Zbl
,[5] An theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa 22 (2) (1995) 240-273. | Numdam | MR | Zbl
, , , , , ,[6] 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 | Zbl
, ,[7] Résultats d'existence pour certains problèmes elliptiques quasilinéaires, Ann. Scuola Norm. Sup. Pisa 11 (1984) 213-235. | Numdam | MR | Zbl
, , ,[8] Existence results for some quasilinear parabolic equations, Nonlinear Anal. 13 (1989) 373-392. | MR | Zbl
, , ,[9] Bounded solutions for a class of quasi-linear parabolic problems with a quadratic gradient term, Progr. Nonlinear Differential Equations 50 (2002) 39-48. | MR | Zbl
, ,[10] 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 | Zbl
, , ,[11] Analyse fonctionnelle. Théorie et applications, Collection Mathématiques Appliquées pour la Maîtrise, Masson, Paris, 1983. | MR | Zbl
,[12] Nonlinear elliptic equations with natural growth in general domains, Ann. Mat. Pura Appl. 181 (2002) 407-426. | MR | Zbl
, , ,[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
[14] Nonlinear parabolic equations with natural growth conditions and data, Nonlinear Anal. 27 (1996) 59-73. | MR | Zbl
, ,[15] Degenerate Parabolic Equations, Springer-Verlag, New York, 1993. | MR | Zbl
,[16] Partial Differential Equations, Graduate Stud. in Math., vol. 19, American Mathematical Society, Providence, RI, 1998. | Zbl
,[17] Nonlinear problems having natural growth in the gradient: an existence result when the source terms are small, Nonlinear Anal. 42 (2000) 1309-1326. | MR | Zbl
, ,[18] -estimates for nonlinear elliptic problems with p-growth in the gradient, J. Ineq. Appl. 3 (1999) 109-125. | MR | Zbl
, , ,[19] Nonlinear parabolic equations with p-growth and unbounded data, C. R. Acad. Sci. Paris Sèr. I Math. 328 (1999) 291-296. | MR | Zbl
, , ,[20] Nonlinear parabolic problems with critical growth and unbounded data, Indiana Univ. Math. J. 50 (3) (2001) 1201-1215. | MR | Zbl
, , ,[21] Linear and Quasi-Linear Equations of Parabolic Type, Transl. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, RI, 1968. | MR | Zbl
, , ,[22] On the existence of weak solutions for quasilinear parabolic boundary value problems, Proc. Roy. Soc. Edinburgh Sect. A 89 (1981) 217-237. | MR | Zbl
,[23] 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 | Zbl
, ,[24] Existence of bounded solutions of some nonlinear parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A 107 (3-4) (1987) 313-326. | MR | Zbl
,[25] -estimate and existence of solutions for some nonlinear parabolic equations, Boll. Un. Math. Ital. B 6 (1992) 631-647. | MR | Zbl
, ,[26] Regularity for entropy solutions of a class of parabolic equations with non regular initial datum, Dynamic Systems Appl. 7 (1998) 53-71. | MR | Zbl
,[27] A. Porretta, S. Segura de León, Nonlinear elliptic equations having a gradient term with natural growth, Preprint.
[28] Existence and uniqueness of entropy solution of parabolic problems with data, Nonlinear Anal. 28 (12) (1997) 1943-1954. | MR | Zbl
,[29] Compact sets in the space , Ann. Mat. Pura Appl. 146 (1987) 65-96. | MR | Zbl
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