@article{AIHPC_2007__24_1_61_0, author = {Andreu, F. and Igbida, N. and Maz\'on, J. M. and Toledo, J.}, 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}, volume = {24}, year = {2007}, pages = {61-89}, doi = {10.1016/j.anihpc.2005.09.009}, mrnumber = {2286559}, zbl = {1123.35016}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2007__24_1_61_0} }
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) pp. 61-89. doi : 10.1016/j.anihpc.2005.09.009. http://gdmltest.u-ga.fr/item/AIHPC_2007__24_1_61_0/
[1] K. Ammar, F. Andreu, J. Toledo, Quasi-linear elliptic problems in with non homogeneous boundary conditions, Rend. Mat. Univ. Roma, in press. | Zbl pre05228267
[2] F. Andreu, N. Igbida, J.M. Mazón, J. Toledo, A degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions, in preparation. | Zbl 1116.35073
[3] Quasi-linear elliptic and parabolic equations in with nonlinear boundary conditions, Adv. Math. Sci. Appl. 7 (1) (1997) 183-213. | MR 1454663 | Zbl 0882.35048
, , , ,[4] Ph. Bénilan, Equations d'évolution dans un espace de Banach quelconque et applications, Thesis, Univ. Orsay, 1972.
[5] An -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 1354907 | Zbl 0866.35037
, , , , , ,[6] A semilinear equation in , Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 2 (4) (1975) 523-555. | Numdam | MR 390473 | Zbl 0314.35077
, , ,[7] 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 1164641 | Zbl 0895.47036
, ,[8] Ph. Bénilan, M.G. Crandall, A. Pazy, Evolution Equations governed by accretive operators, in press.
[9] Some existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions, Appl. Math. Optim. 17 (3) (1988) 203-224. | MR 922980 | Zbl 0652.35043
, , ,[10] Nonlinear elliptic equations with right-hand side measures, Comm. Partial Differential Equations 17 (1992) 641-655. | MR 1163440 | Zbl 0812.35043
, ,[11] Problémes unilatéraux, J. Math. Pures Appl. 51 (1972) 1-168. | MR 428137 | Zbl 0237.35001
,[12] Opérateur Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, Oxford Univ. Press, Oxford, 1984.
,[13] An introduction to evolution governed by accretive operators, in: , (Eds.), Dynamical System, An International Symposium, vol. 1, Academic Press, New York, 1976, pp. 131-165, Dekker, New York, 1991. | MR 636953 | Zbl 0339.35049
,[14] Free and Moving Boundary Problems, North-Holland, Amsterdam, 1977.
,[15] The ill-posed Hele-Shaw model and the Stefan problem for supercooler water, Trans. Amer. Math. Soc. 282 (1984) 183-204. | Zbl 0621.35102
, ,[16] Inequalities in Mechanics and Physiscs, Springer-Verlag, 1976. | MR 600341 | Zbl 0331.35002
, ,[17] A variational inequality approach to the Hele-Shaw flow with a moving boundary, Proc. Roy. Soc. Edinburg Sect. A 88 (1981) 93-107. | Zbl 0455.76043
, ,[18] A degenerate diffusion problem with dynamical boundary conditions, Math. Ann. 323 (2) (2002) 377-396. | MR 1913047 | Zbl 1001.35072
, ,[19] N. Igbida, The Hele-Shaw problem with dynamical boundary conditions, Preprint.
[20] N. Igbida, Nonlinear heat equation with fast/logarithmic diffusion, Preprint.
[21] An Introduction to Variational Inequalities and their Applications, Pure Appl. Math., vol. 88, Academic Press Inc., New York, 1980. | MR 567696 | Zbl 0457.35001
, ,[22] Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal. 12 (1988) 1203-1219. | MR 969499 | Zbl 0675.35042
,[23] Quelques méthodes de résolution de problémes aux limites non linéaires, Dunod-Gauthier-Vilars, Paris, 1968. | Zbl 0189.40603
,