Optimal Concavity of the Torsion Function

Antoine Henrot (), Carlo Nitsch (), Paolo Salani () and Cristina Trombetti ()
Additional contact information
Antoine Henrot: Université de Lorraine - CNRS
Carlo Nitsch: Università degli Studi di Napoli “Federico II”
Paolo Salani: Università degli Studi di Firenze
Cristina Trombetti: Università degli Studi di Napoli “Federico II”

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 1, No 2, 26-35

Abstract: Abstract It is well known that the torsion function of a convex domain has a square root which is concave. The power one half is optimal in the sense that no greater power ensures concavity for every convex set. In this paper, we investigate concavity, not of a power of the torsion function itself, but of the complement to its maximum. Requiring that the torsion function enjoys such a property for the power one half leads to an unconventional overdetermined problem. Our main result is to show that solutions of this problem exist, if and only if they are quadratic polynomials, finding, in fact, a new characterization of ellipsoids.

Keywords: Torsion function; Optimal concavity; Ellipsoids; 35N25; 35R25; 35R30; 35B06; 52A40 (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-018-1302-9 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:178:y:2018:i:1:d:10.1007_s10957-018-1302-9

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

DOI: 10.1007/s10957-018-1302-9

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 ().