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arXiv · 2006.14213

Dimension estimates for the boundary of planar Sobolev extension domains

Danka Lučić·Tapio Rajala·Jyrki Takanen
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Abstract

We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev $W^{1,p}$-extension domains via the weak mean porosity of the boundary. The sharpness of our estimate is shown by examples.

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Danka Lučić, Tapio Rajala, Jyrki Takanen. 2020-06-25. Dimension estimates for the boundary of planar Sobolev extension domains. https://arxiv.org/abs/2006.14213

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