Arkiv för Matematik

  • Ark. Mat.
  • Volume 46, Number 2 (2008), 271-283.

Lipschitz continuity of the Green function in Denjoy domains

Tom Carroll and Stephen J. Gardiner

Full-text: Open access


In this paper a Wiener-type characterization is presented of those boundary points of a Denjoy domain where the Green function is Lipschitz continuous. This property is linked with the splitting of a Euclidean boundary point into two minimal Martin boundary points.

Article information

Ark. Mat., Volume 46, Number 2 (2008), 271-283.

Received: 21 August 2006
First available in Project Euclid: 31 January 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

2008 © Institut Mittag-Leffler


Carroll, Tom; Gardiner, Stephen J. Lipschitz continuity of the Green function in Denjoy domains. Ark. Mat. 46 (2008), no. 2, 271--283. doi:10.1007/s11512-007-0069-2.

Export citation


  • Ancona, A., Une propriété de la compactification de Martin d’un domaine euclidien, Ann. Inst. Fourier (Grenoble) 29:4 (1979), 71–90.
  • Andrievskii, V. V., Positive harmonic functions on Denjoy domains in the complex plane, Preprint, August 2006. arXiv:math/0608643
  • Armitage, D. H. and Gardiner, S. J., Classical Potential Theory, Springer Monogr. Math., Springer, London, 2001.
  • Benedicks, M., Positive harmonic functions vanishing on the boundary of certain domains in Rn, Ark. Mat. 18 (1980), 53–72.
  • Carleson, L. and Totik, V., Hölder continuity of Green’s functions, Acta Sci. Math. (Szeged) 70 (2004), 557–608.
  • Chevallier, N., Frontière de Martin d’un domaine de Rn dont le bord est inclus dans une hypersurface lipschitzienne, Ark. Mat. 27 (1989), 29–48.
  • Domar, Y., On the existence of a largest subharmonic minorant of a given function, Ark. Mat. 3 (1957), 429–440.
  • Gardiner, S. J., Minimal harmonic functions on Denjoy domains, Proc. Amer. Math. Soc. 107 (1989), 963–970.