Fine topology and fine trace on the boundary associated with a class of semilinear differential equations

Communications on Pure and Applied Mathematics

Volumn 51, Issue 8, 1998, Pages 897-936

  Dynkin, E B ^a   Kuznetsov, S E ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032381447     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0312(199808)51:8<897::aid-cpa2>3.0.co;2-0     Document Type: Article

References (27)

1. Bourbaki, N., Éléments de mathématique. IX. Première partie: Les structures fondamentales de l'analyse. Livre IV: Fonctions d'une variable réelle (théorie élémentaire), Actualités Sci. Ind., No. 1074, Hermann, Paris, 1949.
2. Dynkin, E. B., Markov Processes I, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1965.
3. Dynkin, E. B., A probabilistic approach to one class of nonlinear differential equations, Probab. Theory Related Fields 89, 1991, pp. 89-115.
4. Dynkin, E. B., Superdiffusions and parabolic nonlinear differential equations, Ann. Probab. 20, 1992, pp. 942-962.
5. Dynkin, E. B., Superprocesses and partial differential equations, Ann. Probab. 21, 1993, pp. 1185-1262.
6. α, C. R. Acad. Sci. Paris Sér. I Math. 325, 1997, pp. 439-444.
7. α, J. Funct. Anal. 153, 1998, pp. 147-186.
8. Dynkin, E. B., and Kuznetsov, S. E., Superdiffusions and removable singularities for quasilinear partial differential equations, Comm. Pure Appl. Math. 49, 1996, pp. 125-176.
9. α dominated by L-harmonic functions, J. Anal. Math. 68, 1996, pp. 15-37.
10. Dynkin, E. B., and Kuznetsov, S. E., Solutions of nonlinear differential equations on a Riemannian manifold and their trace on the Martin boundary, Trans. Amer. Math. Soc., 1998, to appear.
11. Dynkin, E. B., and Kuznetsov, S. E., Trace on the boundary for solutions of nonlinear differential equations, Trans. Amer. Math. Soc., 1998, to appear.
12. Friedman, A., Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964.
13. Gilbarg, D., and Trudinger, N. S., Elliptic partial differential equations of second order, 2nd ed., Grundlehren der Mathematischen Wissenschaften No. 224, Springer-Verlag, Berlin-New York, 1983.
14. Keller, J. B., On the solutions of Δu = f(u), Comm. Pure Appl. Math. 10, 1957, pp. 503-510.
15. Krasnoselskii, M. A., and Rutickii, Ya. B., Convex Functions and Orlicz Spaces, P. Noordhoff, Groningen, 1961.
16. Kuratowski, K., Topology, Academic Press, New York, 1966.
17. α and fine trace on the boundary, C. R. Acad. Sci. Paris Sér. I Math., 1998, to appear.
18. 2 dans le disque unité, C. R. Acad. Sci. Paris Sér. I Math. 317, 1993, pp. 873-878.
19. 2 in a domain, Probab. Theory Related Fields 102, 1995, pp. 393-432.
20. Le Gall, J.-F., A probabilistic approach to the trace at the boundary for solutions of a semilinear parabolic partial differential equation, J. Appl. Math. Stochastic Anal. 9, 1996, pp. 399-414.
21. 2 in a planar domain, Comm. Pure Appl. Math. 50, 1997, pp. 69-103.
22. Marcus, M., and Véron, L., Trace au bord des solutions positives d'équations elliptiques non linéaires, C. R. Acad. Sci. Paris Sér. I Math. 321, 1995, pp. 179-184.
23. Marcus, M., and Véron, L., Trace au bord des solutions positives d'équations elliptiques et paraboliques non linéaires. Résultats d'existence et d'unicité, C. R. Acad. Sci. Paris Sér. I Math. 323, 1996, pp. 603-608.
24. Marcus, M., and Véron, L., The boundary trace of positive solutions of semilinear elliptic equations II: The supercritical case, 1997, preprint.
25. Marcus, M., and Véron, L., The boundary trace of positive solutions of semilinear elliptic equations I: The subcritical case, Arch. Rational Mech. Anal., 1998, to appear.
26. Osserman, R., On the inequality Δu ≥ f(u), Pacific J. Math. 7, 1957, pp. 1641-1647.
27. Sattinger, D. H., Topics in Stability and Bifurcation Theory, Springer-Verlag, Berlin-New York, 1973.