Uniqueness results and monotonicity properties for strongly nonlinear elliptic variational inequalities

M. Chipot; G. Michaille

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1989)

  • Volume: 16, Issue: 1, page 137-166
  • ISSN: 0391-173X

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Chipot, M., and Michaille, G.. "Uniqueness results and monotonicity properties for strongly nonlinear elliptic variational inequalities." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 16.1 (1989): 137-166. <http://eudml.org/doc/84048>.

@article{Chipot1989,
author = {Chipot, M., Michaille, G.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {uniqueness; monotonicity; variational inequalities},
language = {eng},
number = {1},
pages = {137-166},
publisher = {Scuola normale superiore},
title = {Uniqueness results and monotonicity properties for strongly nonlinear elliptic variational inequalities},
url = {http://eudml.org/doc/84048},
volume = {16},
year = {1989},
}

TY - JOUR
AU - Chipot, M.
AU - Michaille, G.
TI - Uniqueness results and monotonicity properties for strongly nonlinear elliptic variational inequalities
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1989
PB - Scuola normale superiore
VL - 16
IS - 1
SP - 137
EP - 166
LA - eng
KW - uniqueness; monotonicity; variational inequalities
UR - http://eudml.org/doc/84048
ER -

References

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  1. [1] R.A. Adams.Sobolev Spaces, Academic Press, New York (1975). Zbl0314.46030MR450957
  2. [2] M. Artola.Sur une classe de problèmes paraboliques quasilinéaires, Bollettino U.M.I. (6), 5-B (1986), 51-70. Zbl0605.35044MR841617
  3. [3] L. Boccardo.An Ls -Estimate for the Gradient of Solutions of Some Nonlinear Unilateral Problems, Ann. Math. Pura Appl., 141 (1985), 277-287. Zbl0599.49009MR816788
  4. [4] L. Boccardo - F. Murat - J.P. Puel.Existence of bounded solutions for nonlinear elliptic unilateral problems, Preprint, Université Pierre et Marie Curie, (1987). MR980979
  5. [5] H. Brezis.Problèmes unilatéraux, J. Math. Pures et Appl., 51 (1972), 1-168. Zbl0237.35001MR428137
  6. [6] H. Brezis - F.E. Browder.Strongly nonlinear boundary value problems, Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (4) 5 (1978), 587-603. Zbl0453.35029MR507004
  7. [7] H. Brezis - D. Kinderlehrer - G. Stampacchia.Sur une nouvelle formulation du problème de l' écoulement à travers une digue, C.R. Acad. Sc. Paris, Série A, 287 (1978), 711-714. Zbl0391.76072MR515672
  8. [8] J. Carrillo - M. Chipot.On nonlinear elliptic equations involving derivative of the nonlinearity, Proc. Roy. Soc. Edinburgh, 100A (1985), 281-294. Zbl0586.35044MR807707
  9. [9] J. Carrillo.Unicité des solutions du type Kruskov pour des problèmes elliptiques avec des termes de transport non linéaires, C.R. Acad. Sc. Paris, 303, Série I, (1986), 189-192. Zbl0623.35030MR854731
  10. [10] J. Carrillo.On the uniqueness of the solution of a class of elliptic equations with nonlinear convention, Preprint, Universidad complutense, Madrid (1987). Zbl0647.35026MR907721
  11. [11] M. Chipot - G. Michaille.Communication to the Irsee Meeting, (1987), To appear. 
  12. [12] J. DouglasJr. - T. Dupont - J. Serrin.Uniqueness and Comparison Theorems for Nonlinear Elliptic Equations in Divergence Form, Arch. Rational Mech. Anal. (42) (1971), 157-168. Zbl0222.35017MR393829
  13. [13] G. Gagneux.Approximations Lipschitziennes de la fonction signe et schémas semidiscrétisés implicites de problèmes quasi-linéaires dégénérés, Preprint, Université de Besançon. Zbl0571.35046
  14. [14] F. Gastaldi - F. Tomarelli.Some Remarks on Nonlinear and Noncoercive Variational Inequalities, Bollettino U.M.I. (7), 1-B (1987), 143-165. Zbl0624.47053MR895456
  15. [15] D. Gilbarg - N.S. Trudinger.Elliptic Partial Differential Equations of Second Order, Springer-Verlag, New-York (1985). Zbl0361.35003
  16. [16] D. Kinderlehrer - G. Stampacchia.An Introduction to Variational Inequalities, Academic Press, New York (1980). Zbl0457.35001MR567696
  17. [17] J. Leray - J.L. Lions.Quelques resultats de Visik sur les problèmes elliptiques non linéaires par les méthodes de Minty - Browder, Bull. Soc. Math. France, 93 (1965), 97-107. Zbl0132.10502MR194733
  18. [18] J.L. Lions.Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod-Gauthier-Villars (1969). Zbl0189.40603MR259693
  19. [19] G. Michaille.Thesis, Université de Metz, 1988. 
  20. [20] J. Necas.Introduction to the Theory of Nonlinear Elliptic Equations, John WileyInterscience, New York (1986). Zbl0643.35001MR874752
  21. [21] J.M. Rakotoson - R. Temam.Une nouvelle méthode d' estimations L∞. Application aux inéquations variationnelles, C.R. Acad. Sc. Paris, 304, Série I, (1987), 527-530. Zbl0619.46036
  22. [22] J.M. Rakotoson - R. Temam.Relative Rearrangement in Quasilinear Variational Inequalities, Preprint, Université de Paris Sud (1987). MR916743
  23. [23] N.S. Trudinger.On the Comparison Principle for Quasilinear Divergence Structure Equations, Arch. Rational Mech. Anal. (57) 1974, 128-133. Zbl0311.35046MR425353

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