An elliptic semilinear equation with source term involving boundary measures: The subcritical case

Revista Matematica Iberoamericana

Volumn 16, Issue 3, 2000, Pages 477-513

  Bidaut Véron, Marie Francoise ^a,b   Vivier, Laurent ^a,b  

^a UNIVERSITÉ DE TOURS   (France)

^b UNIVERSITÉ DE TOULON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034550715     PISSN: 02132230     EISSN: 22350616     Source Type: Journal    
DOI: 10.4171/RMI/281     Document Type: Article

References (31)

1. Amann, H., Quittner, P., Elliptic boundary value problems involving measures: existence, regularity and multiplicity. Advances in Diff. Equations 3 (1998), 753-813.
2. N). Ann. Scuola Norm. Sup. Pisa 2 (1975), 523-555.
3. Bidaut-Veron, M.-F., Local and global behaviour of solutions of quasilinear equations of Emden-Fowler type. Arch. Rational Mech. Anal. 107 (1989), 293-324.
4. Bidaut-Véron, M.-F., Local behaviour of solutions of a class of nonlinear elliptic systems. Advances in Diff. Equations 5 (2000).
5. Bidaut-Véron, M.-F., Véron, L., Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations. Invent. Math. 106 (1991), 489-539.
6. 1. Unpublished work.
7. Brézis, H., Cabré, X., Some simple nonlinear PDE's without solutions. Boll. Unione Mat. Italiana 8 (1998), 223-262.
8. Brézis, H., Lions, P. L., A note on isolated singularities for linear elliptic equations. Math. Anal. Appl. Adv. Math. Suppl. Stud. 7A (1981), 263-266.
9. Cabré, X., Martel, Y., Weak eigenfunctions for the linearization of extremal elliptic problems. J. Funct. Anal. 156 (1998), 30-56.
10. Caffarelli, L. A., Gidas, B., Spruck, J., Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Comm. Pure Appl. Math. 42 (1989), 271-297.
11. Dautray, R., Lions, J. L., Analyse mathématique et calcul numérique. Masson ed., 1987.
12. De Figuereido, D. G., Lions, P. L., Nussbaum, R. D., A priori estimates and existence of positive solutions of semilinear elliptic equations. J. Math. Pures et Appl. 61 (1982), 41-63.
13. Dynkin, E. B., A probabilistic approach to one class of nonlinear differential equations. Probab. Theor. Relat. Fields 89 (1991), 89-115.
14. Dynkin, E. B., Kuznetzov, S. E., Superdiffusion and removable singularities for quasilinear partial differential equations. Comm. Pure Appl. Math. 49 (1996), 125-176.
15. Geymonat, G., Grisvard, P., Problemi ai limiti lineari ellittici negli spazi di Sobolev con peso. Le Matematiche 22 (1967), 1-38.
16. Gidas, B., Spruck, J., Global and local behavior of positive solutions of nonlinear elliptic equations. Comm. Pure Appl. Math. 34 (1981), 525-598.
17. Gidas, B., Spruck, J., A priori bounds for positive solutions of nonlinear elliptic equations. Comm. Partial Diff. Equations 6 (1981), 883-901.
18. Gilbarg, D., Trudinger, N. S., Elliptic partial differential equations of second order. Springer-Verlag, 1983.
19. Gmira, A., Véron, L., Boundary singularities of solutions of some nonlinear elliptic equations. Duke Math. J. 64 (1991), 271-324.
20. Krantz, S. G., Function theory of several complex variables. 2nd ed., Wadsworth, 1992.
21. 2 dans le disque unité. C. R. Acad. Sci. Paris 317 Série I (1993), 873-878.
22. Lions, P. L., Isolated singularities in semilinear problems. J. Diff. Equations 38 (1980), 441-450.
23. Marcus, M., Véron, L., The boundary trace of positive solutions of semilinear elliptic equations: The subcritical case. Arch. Rational Mech. Anal. 144 (1998), 201-231.
24. Marcus, M., Véron, L., The boundary trace of positive solutions os semilinear elliptic equations: The supercritical case. J. Math. Pures et Appl. 77 (1998), 481-524.
25. Maz'ja, V. G., Beurling's theorem on a minimum principle for positive harmonic functions. J. Sov. Math. 4 (1975), 367-379.
26. Opic, B., Kufner, A., Hardy type inequalities. Pitman Research in Math. Series, Longman Scientific Technical, 1990.
27. Serrin, J., Isolated singularities of solutions of quasilinear equations. Acta Math. 1134 (1964), 247-302.
28. Triebel, H., Interpolation Theory, Function Spaces, Differential Equations. North-Holland, 1978.
29. Véron, L., Singularities of solutions of second order quasilinear equations. Pitman Research Notes in Math. Longman Sci. & Tech. 353, 1996.
30. Véron, L., Singular solutions of some nonlinear elliptic equations. Nonlinear Anal. 5 (1981), 225-242.
31. Widman, K. O., Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations. Math. Scand. 21 (1967), 17-37.