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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Natural limits for harmonic and superharmonic functions

Author: J. R. Diederich
Journal: Trans. Amer. Math. Soc. 224 (1976), 381-397
MSC: Primary 31B25
MathSciNet review: 0419796
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Abstract: In this paper it is shown that Fatou's theorem holds for superharmonic functions in certain Liapunov domains if mean continuous limits are used in place of nontangential limits for which Fatou's theorem fails. Also, existence of mean continuous limits is established for certain semi-linear elliptic equations in Liapunov domains.

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Keywords: Superharmonic, mean continuous limit, nontangential limit, radial limit, Liapunov domain, semilinear elliptic
Article copyright: © Copyright 1976 American Mathematical Society

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