TY - JOUR
T1 - The eigenvalues and eigenfunctions of the non-linear equation associated to second order Sobolev embeddings
AU - Boulton, Lyonell
AU - Lang, Jan
N1 - Funding Information:
This research was funded by The UK's Royal Society International Exchange Grant “James Orthogonality and Higher order Sobolev Embeddings”. We are also grateful to our colleagues at the Czech Technical University in Prague for hosting many of the discussions that eventually lead to this paper. Jan Lang was partially supported by OP RDE project No. CZ.02.2.69/0.0/0.0/18_053/0016976 International mobility of research, technical and administrative staff at the Charles University.
Funding Information:
This research was funded by The UK’s Royal Society International Exchange Grant “James Orthogonality and Higher order Sobolev Embeddings”. We are also grateful to our colleagues at the Czech Technical University in Prague for hosting many of the discussions that eventually lead to this paper. Jan Lang was partially supported by OP RDE project No. CZ.02.2.69/0.0/0.0/18_053/0016976 International mobility of research, technical and administrative staff at the Charles University.
Publisher Copyright:
© 2023
PY - 2023/11
Y1 - 2023/11
N2 - 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.
AB - 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.
KW - Higher order Sobolev embeddings
KW - pq-biLaplacian
KW - s-numbers
UR - http://www.scopus.com/inward/record.url?scp=85168558412&partnerID=8YFLogxK
U2 - 10.1016/j.na.2023.113362
DO - 10.1016/j.na.2023.113362
M3 - Article
AN - SCOPUS:85168558412
SN - 0362-546X
VL - 236
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
M1 - 113362
ER -