On a decomposition of regular domains into John domains with uniform constants - Friedrich, Manuel (Esaim-Control Optimisation and Calculus of Variations, 2018)
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 ΣNj=1 H1(∂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.
CRIS-Team Scopus Importer:2021-10-21
Keywords: Free discontinuity problems; John domains; Korn's inequality; Shape optimization problems