Universität zu Köln

Ferone, Vincenzo, Kawohl, Bernd ORCID: 0000-0003-2918-7318 and Nitsch, Carlo (2018). Generalized elastica problems under area constraint. Math. Res. Lett., 25 (2). S. 521 - 534. SOMERVILLE: INT PRESS BOSTON, INC. ISSN 1945-001X

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Abstract

It was recently proved in [3, 4] that the elastic energy E(gamma) = 1/2 integral(gamma)kappa(2)ds of a closed curve gamma with curvature kappa has a minimizer among all plane, simple, regular and closed curves of given enclosed area A(gamma), and that the minimum is attained only for circles. In particular, the proof used in [4] is of a geometric nature, and here we show under which hypothesis it can be extended to other functionals involving the curvature. As an example we show that the optimal shape remains a circle for the p-elastic energy integral(gamma) vertical bar kappa vertical bar(p)ds, whenever p > 1.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Ferone, Vincenzo UNSPECIFIED UNSPECIFIED UNSPECIFIED Kawohl, Bernd UNSPECIFIED orcid.org/0000-0003-2918-7318 UNSPECIFIED Nitsch, Carlo UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-202485
Journal or Publication Title:	Math. Res. Lett.
Volume:	25
Number:	2
Page Range:	S. 521 - 534
Date:	2018
Publisher:	INT PRESS BOSTON, INC
Place of Publication:	SOMERVILLE
ISSN:	1945-001X
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language ISOPERIMETRIC INEQUALITY; CURVATURE; CURVE Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/20248