Generalized Cranston-McConnell inequalities and Martin boundaries of unbounded domains

Journal d'Analyse Mathematique

Volumn 69, Issue , 1996, Pages 137-152

  Aikawa, Hiroaki ^a   Murata, Minoru ^b  

^a SHIMANE UNIVERSITY   (Japan)

^b TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000801374     PISSN: 00217670     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02787105     Document Type: Article

References (16)

1. H. Aikawa, On the Martin boundary of Lipschitz strips, J. Math. Soc. Japan 38 (1986), 527-541.
2. H. Aikawa, On the upper bounds of Green potentials, Hiroshima Math. J.24 (1994), 607-612.
3. C. Bandle, Isoperimetric Inequalities and Applications, Pitman, London, 1980.
4. R. Bañuelos, On an estimate of Cranston and McConnell for elliptic diffusions in uniform domains, Probab. Theory Related Fields 76 (1987), 311-323.
5. R. Bañuelos, Lifetime and heat kernel estimates in non-smooth domains, in Partial Differential Equations with Minimal Smoothness and Applications (B. Dahlberg et al., eds.), Springer-Verlag, New York, 1992, pp. 37-48.
6. K. L. Chung, The lifetime of conditional Brownian motion in the plane, Ann. Inst. Henri Poincaré 20 (1984), 349-351.
7. M. Cranston and T. R. McConnell, The lifetime of conditioned Brownian motion, Z. Wahrsch. Verw. Gebiete 65 (1983), 1-11.
8. W. K. Hayman and P. B. Kennedy, Subharmonic Functions, Vol. 1, Academic Press, New York, 1976.
9. L. L. Helms, Introduction to Potential Theory, Wiley-Interscience, New York, 1969.
10. D. Ioffe and R. Pinsky, Positive harmonic functions vanishing on the boundary for the Laplacian in unbounded horn-shaped domains, Trans. Amer. Math. Soc. 342 (1994), 773-791.
11. R. S. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc. 49 (1941), 137-172.
12. V. G. Maz'ja, On the relationship between Martin and Euclidean topologies, Soviet Math. Dokl. 18 (1977), 283-286.
13. n, Duke Math. J. 53 (1986), 869-943.
14. M. Murata, On construction of Martin boundaries for second order elliptic equations, Publ. RIMS, Kyoto Univ. 26 (1990), 585-627.
15. Y. Pinchover, On positive solutions of second-order elliptic equations, stability results, and classification, Duke Math. J. 57 (1988), 955-980.
16. Chr. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, 1975.