Neumann Laplacians on domains and operators on associated trees

Academic Article

Abstract

  • Connections are established between the essential specta of the Neumann Laplacian on a domain Ω in ℝ2and a one-term operator of Sturm-Liouville type which is defined naturally on the skeleton, or a generalized ridge, Γ of Ω, when Γ is a tree. Horns, spirals, 'rooms and passages' and domains with fractal boundaries, like the Koch snowflake, are examples of such domains Ω. The analysis hinges on the existence of isometric maps between L2(Ω), H1(Ω) and weighted L2, H1spaces defined on Γ in terms of a Lipschitz map τ which projects Ω onto Γ.
  • Authors

    Published In

    Digital Object Identifier (doi)

    Author List

  • Evans WD; Saito Y
  • Start Page

  • 313
  • End Page

  • 342
  • Volume

  • 51
  • Issue

  • 3