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Transactions of the American Mathematical Society

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Porous sets and null sets for elliptic harmonic measures


Author: Jang-Mei Wu
Journal: Trans. Amer. Math. Soc. 346 (1994), 455-473
MSC: Primary 31B35; Secondary 35J99
DOI: https://doi.org/10.1090/S0002-9947-1994-1260206-0
MathSciNet review: 1260206
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Abstract: We give a genuinely $ n$-dimensional construction of uniformly elliptic operators $ L$ in $ \mathbb{R}_ + ^n$ (of divergence form, and of nondivergence form), which have positive $ L$-harmonic measures on a class of porous sets on $ \partial \mathbb{R}_ + ^n$ with zero surface measure. The porosity condition given is sharp. The earlier methods were all two dimensional.


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DOI: https://doi.org/10.1090/S0002-9947-1994-1260206-0
Article copyright: © Copyright 1994 American Mathematical Society

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