Dimension estimate for the two-sided points of planar Sobolev extension domains-Reference-Cited by-同舟云学术

Dimension estimate for the two-sided points of planar Sobolev extension domains

Published:2023-06-16 Issue: Volume: Page:
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Takanen Jyrki

Abstract

In this paper we give an estimate for the Hausdorff dimension of the set of two-sided points of the boundary of bounded simply connected Sobolev W 1 , p W^{1,p} -extension domain for 1 > p > 2 1>p>2 . Sharpness of the estimate is shown by examples. We also prove the equivalence of different definitions of two-sided points.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/proc/0000-000-00/S0002-9939-2023-16362-5/S0002-9939-2023-16362-5.pdf

Reference22 articles.

1. S. Bechtel, R. M. Brown, R. Haller-Dintelmann, and P. Tolksdorf, Extendability of functions with partially vanishing trace, Preprint, arXiv:1910.06009, 2021.

2. Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets;Bechtel, Sebastian;J. Fourier Anal. Appl.,2019

3. Lebesgue spaces of differentiable functions and distributions;Calderón, A.-P.,1961

4. Sobolev extension property for tree-shaped domains with self-contacting fractal boundary;Deheuvels, Thibaut;Ann. Sc. Norm. Super. Pisa Cl. Sci. (5),2016

5. Cambridge Tracts in Mathematics;Falconer, K. J.,1986

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A necessary condition for Sobolev extension domains in higher dimensions;Nonlinear Analysis;2024-03