On the approximation numbers of Sobolev embeddings on singular domains and trees

Academic Article

Abstract

  • Upper and lower bounds are determined for a function which counts the approximation numbers of the Sobolev embedding W 1,p (Ω)/ℂ → L p(Ω)/ℂ, for a wide class of domains Ω of finite volume in ℝ n and 1 < p < ∞. Results on the distribution of the eigenvalues of the Neumann Laplacian in L 2(Ω) are special consequences.
  • Authors

    Published In

    Digital Object Identifier (doi)

    Author List

  • Evans WD; Harris DJ; Saito Y
  • Start Page

  • 267
  • End Page

  • 302
  • Volume

  • 55
  • Issue

  • 3