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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| Vydané v: | Nonlinear analysis Ročník 236; s. 113362 |
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| Médium: | Journal Article |
| Jazyk: | English |
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01.11.2023
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| ISSN: | 0362-546X, 1873-5215 |
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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 1p+1q=1. Our findings shed new light on the surprising nature of higher order Sobolev spaces in the Banach space setting. |
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| AbstractList | 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. |
| ArticleNumber | 113362 |
| Author | Lang, Jan Boulton, Lyonell |
| Author_xml | – sequence: 1 givenname: Lyonell orcidid: 0000-0001-9945-136X surname: Boulton fullname: Boulton, Lyonell email: L.Boulton@hw.ac.uk organization: Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK – sequence: 2 givenname: Jan orcidid: 0000-0003-1582-7273 surname: Lang fullname: Lang, Jan email: Lang@math.osu.edu organization: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210-1174, USA |
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| Cites_doi | 10.1112/jlms/jdm083 10.1007/s10958-011-0583-4 10.1016/j.jmaa.2016.06.024 10.1112/blms/bdq030 10.1016/j.jat.2011.09.004 10.1007/BF01450021 10.4171/zaa/1453 10.4171/zaa/1630 10.57262/die/1367241475 10.4064/sm-51-3-201-223 10.1070/SM1992v071n02ABEH001404 10.1016/s0294-1449(16)30249-9 10.1007/BF02418013 |
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| Keywords | pq-biLaplacian s-numbers Higher order Sobolev embeddings |
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| Title | The eigenvalues and eigenfunctions of the non-linear equation associated to second order Sobolev embeddings |
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