Boundary trace of the solutions of the prescribed Gaussian curvature equation

Royal Society of Edinburgh - Proceedings A

Volumn 130, Issue 3, 2000, Pages 527-560

  Grillot, Michèle ^a   Véron, Laurent ^a  

^a Faculté des Sciences ^*  (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044519266     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500000299     Document Type: Article

References (29)

1. P. Avilès and R. McOwen. Conformal deformations to constant negative curvature on noncompact Riemannian manifolds. J. Diff. Geom. 27 (1988), 225-239.
2. C. Bandle and M. Marcus. Large solutions of semilinear elliptic equations: existence, uniqueness and asymptotic behavior. J. Analyt. Math. 58 (1992), 9-24.
3. C. Bandle and M. Marcus. Asymptotic behavior of solutions and their derivative for semilinear elliptic problems with blow-up on the boundary. Ann. Inst. H. Poincaré Analyse Non Linéare 12 (1995), 155-171.
4. P. Baras and M. Pierre. Singularités éliminables pour des équations semilinéaires. Ann. Inst. Fourier, Grenoble 34 (1984), 185-206.
5. J. Doob. Classical potential theory and its probabilistic counterpart (Springer, 1984).
6. E. B. Dynkin. A probabilistic approach to one class of nonlinear differential equations. Prob. Theory Relat. Fields 89 (1991), 89-115.
7. E. B. Dynkin and S. E. Kuznetsov. Superdiffusion and removable singularities for quasilinear P.D.E. Commun. Pure Appl. Math. 49 (1995), 125-176.
8. A. Gmira and L. Véron. Boundary singularities of solutions of some nonlinear elliptic equations. Duke Math. J. 64 (1991), 271-324.
9. J. L. Kazdan. Prescribing the curvature on a Riemannian manifold. CBMS Regional Conference Series in Mathematics, vol. 57 (Washington, DC: Conference Board on Mathematics and Science, 1985).
10. J. L. Kazdan and F. M. Warner. Scalar curvature and conformal deformation of Riemannian structure. J. Diff. Geom. 10 (1975), 113-134.
11. J. B. Keller. On solutions of Δu = f(u). Commun. Pure Appl. Math. 10 (1957), 503-510.
12. 2 dans le disque unité. C. R. Acad. Sci. Paris (Ser. I) 317, (1993) 873-878.
13. 2 in a domain. Prob. Theory Rel. Fields 102 (1995), 393-432.
14. J. F. Le Gall. A probabilistic approach to the trace at the boundary for solutions of a semilinear parabolic partial differential equation. J. Appl. Math. Stoch. Analysis 9 (1996), 399-414.
15. J. M. Lee and T. H. Parker. The Yamabe problem. Bull. Am. Math. Soc. 17 (1987), 37-96.
16. M. Marcus and L. Véron. Trace au bord des solutions positives d'équations elliptiques non-linéaires. C. R. Acad. Sci. Paris (Ser. I) 321 (1995), 179-184.
17. M. Marcus and L. Véron. Trace au bord des solutions positives d'équations elliptiques et paraboliques non-linéaires. C. R. Acad. Sci. Paris (Ser. I) 323 (1996), 603-609.
18. M. Marcus and L. Véron. The boundary trace of positive solutions of semilinear elliptic equations. I. The subcritical case. Arch. Ration. Mech. Analysis 144 (1998), 201-231.
19. M. Marcus and L. Véron. The boundary trace of positive solutions of semilinear elliptic equations: the supercritical case. J. Math. Pure Appl. 77 (1998), 481-524.
20. M. Marcus and L. Véron. Initial trace of positive solutions of some nonlinear parabolic equations. Commun. PDE 24 (1999), 1445-1499.
21. N. G. Meyers. A theory of capacities for potential of functions in Lebesgue classes. Math. Scand. 26 (1970), 255-292.
22. R. Osserman. On the inequality Δu ≥ f(u). Pacific J. Math. 7 (1957), 1641-1647.
23. A. Ratto, M. Rigoli and L. Véron. Scalar curvature and conformal deformation of hyperbolic space. J. Funct. Analysis 121 (1994), 15-77.
24. Y. C. Sheu. Removable singularities for solutions of some nonlinear differential equations. Duke Math. J. 74 (1994), 701-711.
25. E. Stein. Singular integrals and differentiability properties of functions (Princeton University Press, 1970).
26. H. Treibel. Interpolation theory, function spaces, differential operators (North-Holland, 1978).
27. J. L. Vazquez and L. Véron. Singularities of elliptic equations with an exponential nonlinearity. Math. Ann. 269 (1984), 119-135.
28. L. Véron. Semilinear elliptic equations with uniform blow-up on the boundary. J. Analyse Math. 59 (1992), 231-250.
29. L. Véron. Singularities of solutions of second order quasilinear equations. Pitman Research Notes in Mathematics, no. 353 (Addison Wesley Longman Inc., 1996).