Natural limits for harmonic and superharmonic functions

Diederich, J. R.

doi:10.1090/S0002-9947-1976-0419796-9

Natural limits for harmonic and superharmonic functions
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by J. R. Diederich

Trans. Amer. Math. Soc. 224 (1976), 381-397

DOI: https://doi.org/10.1090/S0002-9947-1976-0419796-9

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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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