The Hausdorff dimension of elliptic measure—a counterexample to the Oksendahl conjecture in $\textbf {R}^ 2$
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- by Caroline Sweezy PDF
- Proc. Amer. Math. Soc. 116 (1992), 361-368 Request permission
Abstract:
Two counterexamples to the Oksendahl conjecture in ${\mathbb {R}^2}$ for elliptic measure are constructed. It is shown that there exists a strictly elliptic divergence form operator in a specially constructed quasi-disk such that the associated elliptic measure has as its support a set of Hausdorff dimension arbitrarily close to 2. The method is the construction of a quasi-conformal map from a quasi-disk whose boundary has high Hausdorff dimension to the unit disk. The $L$-operator is the pull-back of $\Delta$ on the unit disk.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 361-368
- MSC: Primary 42B25
- DOI: https://doi.org/10.1090/S0002-9939-1992-1161401-5
- MathSciNet review: 1161401