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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On functions subharmonic in a Lipschitz domain


Author: Jang-Mei Gloria Wu
Journal: Proc. Amer. Math. Soc. 68 (1978), 309-316
MSC: Primary 31B25
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.


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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