Toward a geometric characterization of intrinsic ultracontractivity for Dirichlet Laplacians

Michigan Mathematical Journal

Volumn 47, Issue 1, 2000, Pages 79-99

  Méndez Hernández, Pedro J ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040193841     PISSN: 00262285     EISSN: None     Source Type: Journal    
DOI: 10.1307/mmj/1030374669     Document Type: Article

References (19)

1. n, J. London Math. Soc. (2) 34 (1986), 274-290.
2. R. Bañuelos, Intrinsic ultracontractivity and eigenvalue estimates for Schrödinger operators, J. Funct. Anal. 100 (1991), 181-206.
3. _, Lifetime and heat kernel estimates in non-smooth domains, IMA Vol. Math. Appl., 42, pp. 37-48, Springer, New York, 1992.
4. _, Lifetime of conditioned Brownian motion and related estimates for heat kernels, eigenfunctions and eigenvalues in Euclidean domains, MSRI Lectures, 1998 (http://www.msri.org/publications/In/index,html).
5. R. Bañuelos and T. Carroll, Conditioned Brownian motion and hyperbolic-geodesics in simply connected domains, Michigan Math. J. 40 (1993), 321-331.
6. R. Bañuelos and B. Davis, Heat kernel, eigenfunctions, and conditioned Brownian motion in planar domains, J. Funct. Anal. 84 (1989), 188-200.
7. _, A geometrical characterization of intrinsic ultracontractivity for planar domains with boundaries given by the graphs of functions, Indiana Univ. Math. J. 41 (1992), 885-913.
8. R. F. Bass and K. Burdzy, Lifetimes of conditioned diffusions, Probab. Theory Related Fields 91 (1992), 405-443.
9. R. Coornaert and A. Papadopolous, Symbolic dynamics and hyperbolic groups, Lecture Notes in Math., 1539, Springer-Verlag, Berlin, 1993.
10. E. B. Davies, Heat kernels and spectral theory, Cambridge Univ. Press, Cambridge, 1989.
11. E. B. Davies and B. Simon, Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. Funct. Anal, 59 (1984), 335-395.
12. B. Davis, Conditioned Brownian motion in planar domains, Duke Math. J. 57 (1988), 397-421.
13. P. S. Griffin, G, C. Verchota, and A. L. Vogel, Distortion of the area and conditioned Brownian motion, Probab. Theory Related Fields 96 (1993), 385-413.
14. W. K. Hayman, Subharmonic functions, vol. 2, London Math. Soc. Monographs, 20, Academic Press, London, 1989.
15. G. Martin, Quasiconformal and bi-Lipschitz homeomorphisms, uniform domains and the quasihyperbolic metric, Trans. Amer. Math. Soc. 292 (1985), 169-191.
16. Ch, Pommerenke, Univalent functions, Vandenhoeck and Ruprecht, Göttingen, 1975.
17. R. Smits, Conditional Brownian motion, spectral gaps and rates to equilibrium of diffusions, Ph.D. dissertation, Purdue University, 1996.
18. _, Necessary and sufficient conditions for finiteness of lifetimes, Potential Theory 5 (1996), 513-521.
19. E. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, NJ, 1970.