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

Lyonell Boulton*, Jan Lang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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
Article number113362
JournalNonlinear Analysis, Theory, Methods and Applications
Volume236
Early online date22 Aug 2023
DOIs
Publication statusPublished - Nov 2023

Keywords

  • Higher order Sobolev embeddings
  • pq-biLaplacian
  • s-numbers

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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