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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An example on null sets of parabolic measures


Author: Jang-Mei Wu
Journal: Proc. Amer. Math. Soc. 107 (1989), 949-961
MSC: Primary 35K20; Secondary 31A25
DOI: https://doi.org/10.1090/S0002-9939-1989-0986653-3
MathSciNet review: 986653
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Abstract: A set $ E$ on the real line of Hausdorff dimension 1 is constructed, such that the graph of $ E$ on the boundary of any $ {C^2}$ domain $ \left\{ {t > \tau (x)} \right\}$, or on the boundary of any $ {\text{Lip}}\tfrac{1}{2}$ domain $ \left\{ {x > \chi (t)} \right\}$, is null with respect to the parabolic measure associated with any parabolic operator $ L = a(x,t){\partial ^2}/\partial {x^2} - \partial /\partial t$ on $ {{\mathbf{R}}^2};a$ is Hölder continuous and $ 0 < {\Lambda _1} \leq a \leq {\Lambda _2} < \infty $ for some constants $ {\Lambda _1}$ and $ {\Lambda _2}$.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0986653-3
Article copyright: © Copyright 1989 American Mathematical Society