|Publication ahead of print|
|Published online||04 December 2018|
On a decomposition of regular domains into John domains with uniform constants
Faculty of Mathematics, University of Vienna,
1090 Vienna, Austria.
Accepted: 23 March 2017
We derive a decomposition result for regular, two-dimensional domains into John domains with uniform constants. We prove that for every simply connected domain Ω ⊂ ℝ2 with C1-boundary there is a corresponding partition Ω = Ω1 ⋃ … ⋃ ΩN with Σj=1NH1(∂Ωj\∂Ω)≤θ such that each component is a John domain with a John constant only depending on θ. The result implies that many inequalities in Sobolev spaces such as Poincaré’s or Korn’s inequality hold on the partition of Ω for uniform constants, which are independent of Ω.
Mathematics Subject Classification: 26D10 / 70G75 / 46E35
Key words: John domains / Korn’s inequality / free discontinuity problems / shape optimization problems
© EDP Sciences, SMAI 2018
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.