First eigenvalues and comparison of Green's functions for elliptic operators on manifolds or domains

Journal d'Analyse Mathematique

Volumn 72, Issue , 1997, Pages 45-92

  Ancona, Alano ^a  

^a Univ des Sciences Paris Sud   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002417396     PISSN: 00217670     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02843153     Document Type: Article

References (40)

1. A. Ancona, Comparaison des fonctions de Green et des mesures harmoniques pour des opérateurs elliptiques, C. R. Acad. Sci. Paris 294 (1982), 505-508.
2. N, J. London Math. Soc. 34 (2) (1986), 274-290.
3. A. Ancona, Negatively curved manifolds, elliptic operators and the Martin boundary, Ann. of Math. 125 (1987), 495-536.
4. A. Ancona, Théorie du potentiel sur les graphes et les variétés, Ecole d'été de Probabilités de Saint-Flour XVIII - 1988, Lecture Notes in Math. 1427, Springer-Verlag, Berlin, 1990, pp. 5-112.
5. A. Ancona, Positive harmonic functions and hyperbolicity, in Potential Theory, Surveys and Problems, Lecture Notes in Math. 1344, Springer-Verlag, Berlin, 1988, pp. 1-23.
6. D. G. Aronson, Bounds for the fundamental solution of a parabolic equation, Bull. Amer. Math. Soc. 73 (1967), 890-896.
7. H. Berestycki, L. Nirenberg and S. R. S. Varadhan, The principal eigenvalue and maximum principle for second order elliptic operators in general domains, Comm. Pure Appl. Math. 47 (1994), 47-92.
8. M. Brelot, Axiomatique des fonctions harmoniques, Les Presses de l'Université de Montréal, 1969.
9. L. Carleson, On mappings conformal at the boundary, J. Analyse Math. 19 (1967), 1-13.
10. M. Cranston and Z. Zhao, Conditional transformation of drift formula and Potential Theory for 1/2Δ + b(.).∇, Comm. Math. Phys. 112 (1987), 613-627.
11. B. Dahlberg, On the absolute continuity of elliptic measures, Amer. J. Math. 108 (1986), 1119-1138.
12. E. Fabes, C. Kenig and D. Jerison, Necessary and sufficient conditions for absolute continuity of elliptic-harmonic measure, Ann. of Math. 119 (1984), 121-141.
13. R. A. Fefferman, C. Kenig and J. Pipher, The theory of weight and the Dirichlet problem for elliptic equations, Ann. of Math. 134 (1991), 65-124.
14. S. J. Gardiner and M. Klimek, Convexity and subsolutions of partial differential equations, Bull. London Math. Soc. 18 (1986), 41-43.
15. M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Annals of Math. Studies 105, Princeton University Press, Princeton, N.J., 1983.
16. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1977.
17. U. Hamenstädt, Harmonic measures for compact negatively curved manifolds, Preprint, Bonn Universität (1995).
18. R.-M. Hervé, Recherche sur la théorie axiomatique des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier XII (1962), 415-471.
19. M. Hervé and R.-M. Hervé, Les fonctions surharmoniques associées à un opérateur elliptique du second ordre à coefficients discontinus, Ann. Inst. Fourier XIX (1969), 305-359.
20. H. Hueber and M. Sieveking, On the quotients of Green functions, Ann. Inst. Fourier 32 (1) (1982), 105-118.
21. O. A. Ladyzhenskaia and N. N. Uraltseva, Linear and Quasi-Linear Equations, Academic Press, New York and London, 1968.
22. p-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa 17 (1963), 189-206.
23. G. Mokobodzki, Algèbre des multiplicateurs d'un espace de Dirichlet, to appear.
24. n, Duke Math. J. 53 (1986), 869-943.
25. J. Nečas, Les méthodes directes en théorie des opérateurs elliptiques, Masson (Paris), Academia (Prague), 1967.
26. R. Näkki and J. Väisälä, John disks, Exposition. Math. 9 (1991), 3-43.
27. Y. Pinchover, Sur les solutions positives d'équations elliptiques et paraboliques, C. R. Acad. Sci. Paris 302 (1986), 447-450.
28. Y. Pinchover, On positive solutions of second order elliptic equations, stability results and classification, Duke Math. J. 57 (1988), 955-980.
29. Y. Pinchover, Criticality and ground states of second order elliptic equations, J. Differential Equations 80 (1989), 237-250.
30. n, Differential Integral Equations 5 (1992), 481-490.
31. L. Saloff-Coste, Uniformly elliptic operators on Riemannian manifolds, J. Differential Geom. 36 (1992), 417-450.
32. L. Saloff-Coste, Parabolic Harnack inequality for divergence form second order differential operators, Potential Analysis 4 (4) (1995), 429-467.
33. J. Serrin, On the Harnack inequality for linear elliptic equations, J. Analyse Math. 4 (1956), 292-308.
34. G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier 15(1)(1965), 189-258.
35. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, N.J., 1970.
36. J. C. Taylor, The Martin boundaries of equivalent sheaves, Ann. Inst. Fourier 20 (1) (1970), 433-456.
37. K.-O. Widman, On the boundary behavior of solutions to a class of elliptic partial differential equations, Ark. Mat. 6 (1967), 485-533.
38. K.-O. Widman, Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations. Math. Scand. 21 (1967), 17-37.
39. Z. Zhao, Subcriticality, positivity and gaugeability of the Schrödinger operator, Bull. Amer. Math Soc. 23 (1990), 513-517.
40. Z. Zhao, Subcriticality and gaugeability of the Schrödinger operator, Trans. Amer. Math. Soc. 334 (1992), 75-96.