Volume 24, Number 4, October–December 2018
|Page(s)||1541 - 1583|
|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
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