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...

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Veröffentlicht in:Nonlinear analysis Jg. 236; S. 113362
Hauptverfasser: Boulton, Lyonell, Lang, Jan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.11.2023
Schlagworte:
Higher order Sobolev embeddings
pq-biLaplacian
s-numbers
pq-biLaplacian
s-numbers
Higher order Sobolev embeddings
ISSN:0362-546X, 1873-5215
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Zusammenfassung: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