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On functions subharmonic in a Lipschitz domain


Author: Jang-Mei Gloria Wu
Journal: Proc. Amer. Math. Soc. 68 (1978), 309-316
MSC: Primary 31B25
DOI: https://doi.org/10.1090/S0002-9939-1978-0470234-7
MathSciNet review: 0470234
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Abstract: Let D be a starlike Lipschitz domain in $ {R^n},n \geqslant 2$. If w is a subharmonic function in D with positive harmonic majorant, then at almost every point on the boundary of D (surface measure), w has radial limit. Results on limits along certain $ {C^1}$ curves in general Lipschitz domains are also obtained.


References [Enhancements On Off] (What's this?)

  • [1] B. Dahlberg, On estimates of harmonic measure, Arch. Rational Mech. Anal. 65 (1977), 275-288. MR 0466593 (57:6470)
  • [2] J. R. Diederich, Natural limits for harmonic and superharmonic functions, Trans. Amer. Math. Soc. 224 (1976), 381-397. MR 0419796 (54:7814)
  • [3] L. L. Helms, Introduction to potential theory, Wiley, New York, 1969. MR 0261018 (41:5638)
  • [4] R. A. Hunt and R. L. Wheeden, On the boundary values of harmonic functions, Trans. Amer. Math. Soc. 132 (1968), 307-322. MR 0226044 (37:1634)
  • [5] O. D. Kellogg, On the derivatives of harmonic functions on the boundary, Trans. Amer. Math. Soc. 33 (1931), 486-510. MR 1501602
  • [6] J. E. Littlewood, On functions subharmonic in a circle. II, Proc. London Math. Soc. (2) 28 (1928), 383-394.
  • [7] M. L. Silverstein and R. L. Wheeden, Superharmonic functions on Lipschitz domains, Studia Math. 39 (1971), 191-198. MR 0315150 (47:3699)
  • [8] J.-M. Wu, Boundary limits of Green's potentials along curves, Studia Math. 60 (1976), 137-144.
  • [9] -, Boundary limits of Green's potentials along curves. II. Lipschitz domains, Studia Math. (to appear).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0470234-7
Keywords: Subharmonic, Green's potential, harmonic measure, Lipschitz domain, limits along curves, Harnack's inequality, maximum principle
Article copyright: © Copyright 1978 American Mathematical Society

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