On functions subharmonic in a Lipschitz domain

Wu, Jang-Mei Gloria

doi:10.1090/S0002-9939-1978-0470234-7

On functions subharmonic in a Lipschitz domain
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Proc. Amer. Math. Soc. 68 (1978), 309-316 Request permission

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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On functions subharmonic in a circle

28

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Boundary limits of Green’s potentials along curves

60

Boundary limits of Green’s potentials along curves

Lipschitz domains