${L}^{1}$ existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions

Andreu, F.; Igbida, N.; Mazón, J. M.; Toledo, J.

doi:10.1016/j.anihpc.2005.09.009

L^{1}

existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions

Andreu, F. ; Igbida, N. ; Mazón, J. M. ; Toledo, J.

Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 1, pp. 61-89.

MR Zbl | 1 citation dans Numdam

DOI : 10.1016/j.anihpc.2005.09.009

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     title = {${L}^{1}$ existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {61--89},
     publisher = {Elsevier},
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Andreu, F.; Igbida, N.; Mazón, J. M.; Toledo, J. ${L}^{1}$ existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 1, pp. 61-89. doi : 10.1016/j.anihpc.2005.09.009. https://www.numdam.org/articles/10.1016/j.anihpc.2005.09.009/

Bibliographie
Cité par

[1] K. Ammar, F. Andreu, J. Toledo, Quasi-linear elliptic problems in $L^{1}$ with non homogeneous boundary conditions, Rend. Mat. Univ. Roma, in press.

[2] F. Andreu, N. Igbida, J.M. Mazón, J. Toledo, A degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions, in preparation. | Zbl

[3] Andreu F., Mazón J.M., Segura De León S., Toledo J., Quasi-linear elliptic and parabolic equations in $L^{1}$ with nonlinear boundary conditions, Adv. Math. Sci. Appl. 7 (1) (1997) 183-213. | MR | Zbl

[4] Ph. Bénilan, Equations d'évolution dans un espace de Banach quelconque et applications, Thesis, Univ. Orsay, 1972.

[5] Bénilan Ph., Boccardo L., Gallouët Th., 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 Cl. Sci. (4) 22 (2) (1995) 241-273. | Numdam | MR | Zbl

[6] Benilan Ph., Brezis H., Crandall M.G., A semilinear equation in $L^{1} (R^{N})$ , Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 2 (4) (1975) 523-555. | Numdam | MR | Zbl

[7] Bénilan Ph., Crandall M.G., Completely accretive operators, in: Semigroup Theory and Evolution Equations, Delft, 1989, Lecture Notes in Pure and Appl. Math., vol. 135, Dekker, New York, 1991, pp. 41-75. | MR | Zbl

[8] Ph. Bénilan, M.G. Crandall, A. Pazy, Evolution Equations governed by accretive operators, in press.

[9] Bénilan Ph., Crandall M.G., Sacks P., Some $L^{1}$ existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions, Appl. Math. Optim. 17 (3) (1988) 203-224. | MR | Zbl

[10] Boccardo L., Gallouët Th., Nonlinear elliptic equations with right-hand side measures, Comm. Partial Differential Equations 17 (1992) 641-655. | MR | Zbl

[11] Brezis H., Problémes unilatéraux, J. Math. Pures Appl. 51 (1972) 1-168. | MR | Zbl

[12] Brezis H., Opérateur Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, Oxford Univ. Press, Oxford, 1984.

[13] Crandall M.G., An introduction to evolution governed by accretive operators, in: Cesari L., (Eds.), Dynamical System, An International Symposium, vol. 1, Academic Press, New York, 1976, pp. 131-165, Dekker, New York, 1991. | MR | Zbl

[14] Crank J., Free and Moving Boundary Problems, North-Holland, Amsterdam, 1977.

[15] Dibenedetto E., Friedman A., The ill-posed Hele-Shaw model and the Stefan problem for supercooler water, Trans. Amer. Math. Soc. 282 (1984) 183-204. | Zbl

[16] Duvaux G., Lions J.L., Inequalities in Mechanics and Physiscs, Springer-Verlag, 1976. | MR | Zbl

[17] Elliot C.M., Janosky V., A variational inequality approach to the Hele-Shaw flow with a moving boundary, Proc. Roy. Soc. Edinburg Sect. A 88 (1981) 93-107. | Zbl

[18] Igbida N., Kirane M., A degenerate diffusion problem with dynamical boundary conditions, Math. Ann. 323 (2) (2002) 377-396. | MR | Zbl

[19] N. Igbida, The Hele-Shaw problem with dynamical boundary conditions, Preprint.

[20] N. Igbida, Nonlinear heat equation with fast/logarithmic diffusion, Preprint.

[21] Kinderlehrer D., Stampacchia G., An Introduction to Variational Inequalities and their Applications, Pure Appl. Math., vol. 88, Academic Press Inc., New York, 1980. | MR | Zbl

[22] Lieberman G.M., Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal. 12 (1988) 1203-1219. | MR | Zbl

[23] Lions J.L., Quelques méthodes de résolution de problémes aux limites non linéaires, Dunod-Gauthier-Vilars, Paris, 1968. | Zbl

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