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

 Access to full text

 Full (PDF)

1. [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. Zbl1153.35026
2. [2] F. Andreu, N. Igbida, J.M. Mazón, J. Toledo, A degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions, in preparation. Zbl1116.35073
3. [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. Zbl0882.35048MR1454663
4. [4] Ph. Bénilan, Equations d'évolution dans un espace de Banach quelconque et applications, Thesis, Univ. Orsay, 1972. 
5. [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. Zbl0866.35037MR1354907
6. [6] Benilan Ph., Brezis H., Crandall M.G., A semilinear equation in $L^1\left(R^N\right)$, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)2 (4) (1975) 523-555. Zbl0314.35077MR390473
7. [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. Zbl0895.47036MR1164641
8. [8] Ph. Bénilan, M.G. Crandall, A. Pazy, Evolution Equations governed by accretive operators, in press. Zbl0895.47036
9. [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. Zbl0652.35043MR922980
10. [10] Boccardo L., Gallouët Th., Nonlinear elliptic equations with right-hand side measures, Comm. Partial Differential Equations17 (1992) 641-655. Zbl0812.35043MR1163440
11. [11] Brezis H., Problémes unilatéraux, J. Math. Pures Appl.51 (1972) 1-168. Zbl0237.35001MR428137
12. [12] Brezis H., Opérateur Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, Oxford Univ. Press, Oxford, 1984. 
13. [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. Zbl0339.35049MR636953
14. [14] Crank J., Free and Moving Boundary Problems, North-Holland, Amsterdam, 1977. 
15. [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. Zbl0621.35102
16. [16] Duvaux G., Lions J.L., Inequalities in Mechanics and Physiscs, Springer-Verlag, 1976. Zbl0331.35002MR600341
17. [17] Elliot C.M., Janosky V., A variational inequality approach to the Hele–Shaw flow with a moving boundary, Proc. Roy. Soc. Edinburg Sect. A88 (1981) 93-107. Zbl0455.76043
18. [18] Igbida N., Kirane M., A degenerate diffusion problem with dynamical boundary conditions, Math. Ann.323 (2) (2002) 377-396. Zbl1001.35072MR1913047
19. [19] N. Igbida, The Hele–Shaw problem with dynamical boundary conditions, Preprint. Zbl1127.35023
20. [20] N. Igbida, Nonlinear heat equation with fast/logarithmic diffusion, Preprint. 
21. [21] Kinderlehrer D., Stampacchia G., An Introduction to Variational Inequalities and their Applications, Pure Appl. Math., vol. 88, Academic Press Inc., New York, 1980. Zbl0457.35001MR567696
22. [22] Lieberman G.M., Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal.12 (1988) 1203-1219. Zbl0675.35042MR969499
23. [23] Lions J.L., Quelques méthodes de résolution de problémes aux limites non linéaires, Dunod–Gauthier-Vilars, Paris, 1968. Zbl0189.40603