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arXiv · 1209.3602

On the extension property of Reifenberg-flat domains

Antoine Lemenant·Emmanouil Milakis·Laura V. Spinolo
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Abstract

We provide a detailed proof of the fact that any domain which is sufficiently flat in the sense of Reifenberg is also Jones-flat, and hence it is an extension domain. We discuss various applications of this property, in particular we obtain L^\infty estimates for the eigenfunctions of the Laplace operator with Neumann boundary conditions. We also compare different ways of measuring the "distance" between two sufficiently close Reifenberg-flat domains. These results are pivotal to the quantitative stability analysis of the spectrum of the Neumann Laplacian performed in another paper by the same authors.

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Antoine Lemenant, Emmanouil Milakis, Laura V. Spinolo. 2012-09-17. On the extension property of Reifenberg-flat domains. https://arxiv.org/abs/1209.3602

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