Dimension estimates for the boundary of planar Sobolev extension domains-Reference-Cited by-同舟云学术

Dimension estimates for the boundary of planar Sobolev extension domains

Published:2021-12-01 Issue:0 Volume:0 Page:
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Lučić Danka¹,Rajala Tapio¹^ORCID,Takanen Jyrki¹

Affiliation:

1. Department of Mathematics and Statistics , University of Jyvaskyla , P.O. Box 35 (MaD) , Jyvaskyla , Finland

Abstract

Abstract We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev W 1 , p

{W^{1,p}}

-extension domains via the weak mean porosity of the boundary. The sharpness of our estimate is shown by examples.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2021-0042/pdf

Reference12 articles.

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5. P. Koskela, T. Rajala and Y. R.-Y. Zhang, A geometric characterization of planar Sobolev extension domains, preprint (2015), https://arxiv.org/abs/1502.04139.

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