On the approximation numbers of Sobolev embeddings on singular domains and trees
W. D. Evans · The Quarterly Journal of Mathematics · 2004
Upper and lower bounds are determined for a function which counts the approximation numbers of the Sobolev embedding W1,p (Ω)/C ↪Lp (Ω)/C, for a wide class of domains Ω of finite volume in Rn and 1 < p < ∞. Results on the distribution of the eigenvalues of the Neumann Laplacian in L2(Ω) are special consequences.