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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

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Volume 4, Issue 3


A selection criterion of solutions to a system of eikonal equations

Gisella Croce
  • Laboratoire de Mathématiques Appliquées du Havre, Université du Havre, 25, rue Philippe Lebon, 76063 Le Havre, France.
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/ Giovanni Pisante
Published Online: 2010-11-18 | DOI: https://doi.org/10.1515/acv.2011.003


In this article we consider a system of eikonal equations with a Dirichlet boundary condition. We propose a variational method to select the class of solutions which minimize the discontinuity set of the gradient.

Keywords.: Eikonal equation; almost everywhere solutions; special functions of bounded variation; direct methods of the calculus of variations

About the article

Received: 2010-04-08

Revised: 2010-09-03

Published Online: 2010-11-18

Published in Print: 2011-06-01

Citation Information: Advances in Calculus of Variations, Volume 4, Issue 3, Pages 309–338, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv.2011.003.

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Gisella Croce and Giovanni Pisante
Calculus of Variations and Partial Differential Equations, 2017, Volume 56, Number 4

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