Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board: Armstrong, Scott N. / Balogh, Zoltán / Cardiliaguet, Pierre / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Gianazza, Ugo / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / Mingione, Giuseppe / Nystrom, Kaj / Riviére, Tristan / Schaetzle, Reiner / Shen, Zhongwei / Silvestre, Luis / Tonegawa, Yoshihiro / Touzi, Nizar / Wang, Guofang

IMPACT FACTOR 2018: 2.316

CiteScore 2018: 1.77

SCImago Journal Rank (SJR) 2018: 2.350
Source Normalized Impact per Paper (SNIP) 2018: 1.465

Mathematical Citation Quotient (MCQ) 2018: 1.44

See all formats and pricing
More options …
Volume 8, Issue 2


Regularity theory for tangent-point energies: The non-degenerate sub-critical case

Simon Blatt / Philipp Reiter
Published Online: 2014-03-25 | DOI: https://doi.org/10.1515/acv-2013-0020


In this article we introduce and investigate a new two-parameter family of knot energies TP(p,q) that contains the tangent-point energies. These energies are obtained by decoupling the exponents in the numerator and denominator of the integrand in the original definition of the tangent-point energies. We will first characterize the curves of finite energy TP(p,q) in the sub-critical range p ∈ (q+2,2q+1) and see that those are all injective and regular curves in the Sobolev–Slobodeckiĭ space W(p-1)/q,q(/,n). We derive a formula for the first variation that turns out to be a non-degenerate elliptic operator for the special case q = 2: a fact that seems not to be the case for the original tangent-point energies. This observation allows us to prove that stationary points of TP(p,2) + λ length, p ∈ (4,5), λ > 0, are smooth – so especially all local minimizers are smooth.

Keywords: Knot energies; existence of minimizers; regularity theory

MSC: 49N60; 49J10

About the article

Received: 2013-09-12

Revised: 2014-02-06

Accepted: 2014-02-14

Published Online: 2014-03-25

Published in Print: 2015-04-01

Funding Source: Swiss National Science Foundation

Award identifier / Grant number: 200020_125127

Funding Source: Leverhulm trust

Funding Source: DFG Transregional Collaborative Research Centre

Award identifier / Grant number: SFB TR 71

Funding Source: Czech Ministry of Education

Award identifier / Grant number: ERC CZ LL1203

Citation Information: Advances in Calculus of Variations, Volume 8, Issue 2, Pages 93–116, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2013-0020.

Export Citation

© 2015 by De Gruyter.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

James H von Brecht and Ryan Blair
Journal of Physics A: Mathematical and Theoretical, 2017, Volume 50, Number 47, Page 475203

Comments (0)

Please log in or register to comment.
Log in