The eigenvalues and eigenfunctions of the non-linear equation associated to second order Sobolev embeddings

Lyonell Boulton, Jan Lang

Research output: Working paperPreprint

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Abstract

We consider the non-linear eigenvalue equations characterizing Lp into Lq Sobolev embeddings of second order for Navier boundary conditions at both ends of a line segment. We give a complete description of the s-numbers and the extremal functions in the general case (p,q)∈(1,∞)2. Among other results, we show that these can be expressed in terms of those of related first order embeddings, if and only if [Formula presented]. Our findings shed new light on the surprising nature of higher order Sobolev spaces in the Banach space setting.
Original languageEnglish
PublisherarXiv
Publication statusPublished - 10 Apr 2022

Keywords

  • math.CA
  • math.FA
  • math.SP

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