Two Estimates for the First Robin Eigenvalue of the Finsler Laplacian with Negative Boundary Parameter

Gloria Paoli () and Leonardo Trani ()
Additional contact information
Gloria Paoli: Università degli Studi di Napoli Federico II
Leonardo Trani: Università degli Studi di Napoli Federico II

Journal of Optimization Theory and Applications, 2019, vol. 181, issue 3, No 3, 743-757

Abstract: Abstract We prove two bounds for the first Robin eigenvalue of the Finsler Laplacian with negative boundary parameter in the planar case. In the constant area problem, we show that the Wulff shape is a maximizer only for values of the boundary parameter, which are close to zero. In the fixed perimeter case, we prove that the Wulff shape is a maximizer of the first eigenvalue for all values of the boundary parameter.

Keywords: Eigenvalue optimization; Finsler Laplacian; Robin boundary condition; Negative parameter; Wulff shape; 58J50; 35P15 (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-019-01487-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:181:y:2019:i:3:d:10.1007_s10957-019-01487-x

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-019-01487-x

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().