Porous sets and null sets for elliptic harmonic measures
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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.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- 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