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

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...

Full description

Saved in:

Bibliographic Details
Published in:	Nonlinear analysis Vol. 236; p. 113362
Main Authors:	Boulton, Lyonell, Lang, Jan
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.11.2023
Subjects:	Higher order Sobolev embeddings pq-biLaplacian s-numbers pq-biLaplacian s-numbers Higher order Sobolev embeddings
ISSN:	0362-546X, 1873-5215
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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 1p+1q=1. Our findings shed new light on the surprising nature of higher order Sobolev spaces in the Banach space setting.
ISSN:	0362-546X 1873-5215
DOI:	10.1016/j.na.2023.113362