On a decomposition of regular domains into John domains with uniform constants

Friedrich M (2018)

Publication Type: Journal article

Publication year: 2018

Journal

Esaim-Control Optimisation and Calculus of Variations EDP Sciences

Book Volume: 24

Pages Range: 1541-1583

Journal Issue: 4

DOI: 10.1051/cocv/2017029

Abstract

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.

Authors with CRIS profile

Manuel Friedrich

Involved external institutions

Universität Wien / University of Vienna AT Austria (AT)

How to cite

APA:

Friedrich, M. (2018). On a decomposition of regular domains into John domains with uniform constants. Esaim-Control Optimisation and Calculus of Variations, 24(4), 1541-1583. https://doi.org/10.1051/cocv/2017029

MLA:

Friedrich, Manuel. "On a decomposition of regular domains into John domains with uniform constants." Esaim-Control Optimisation and Calculus of Variations 24.4 (2018): 1541-1583.

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