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

Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

Online
ISSN
1435-5345
See all formats and pricing
More options …
Volume 2009, Issue 635

Issues

A singular energy minimizing free boundary

Daniela De Silva / David Jerison
Published Online: 2009-07-30 | DOI: https://doi.org/10.1515/CRELLE.2009.074

Abstract

We consider the problem of minimizing the energy functional ∫(|∇u|2 + χ {u>0}). We show that the singular axissymmetric critical point of the functional is an energy minimizer in dimension 7. This is the first example of a non-smooth energy minimizer. It is analogous to the Simons cone, a least area hypersurface in dimension 8.

About the article

Received: 2006-04-04

Published Online: 2009-07-30

Published in Print: 2009-10-01


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2009, Issue 635, Pages 1–21, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2009.074.

Export Citation

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.

[1]
Guy David, Max Engelstein, and Tatiana Toro
Advances in Mathematics, 2019, Volume 350, Page 1109
[2]
Yang Yang and Kanishka Perera
Nonlinear Analysis, 2019, Volume 180, Page 75
[3]
Yong Liu, Kelei Wang, and Juncheng Wei
Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 2017
[4]
Max Engelstein
Communications in Partial Differential Equations, 2017
[5]
Mark Allen
Journal of Differential Equations, 2017
[6]
David Jerison and Kanishka Perera
The Journal of Geometric Analysis, 2017
[7]
Dario Mazzoleni, Susanna Terracini, and Bozhidar Velichkov
Geometric and Functional Analysis, 2017, Volume 27, Number 2, Page 373
[8]
Lizhou Wang
Communications in Contemporary Mathematics, 2016, Volume 18, Number 03, Page 1650010
[9]
David Jerison and Ovidiu Savin
Geometric and Functional Analysis, 2015, Volume 25, Number 4, Page 1240
[10]
Tanguy Briançon and Jimmy Lamboley
Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 2009, Volume 26, Number 4, Page 1149
[11]
Lizhou Wang and Guanghao Hong
Journal of Mathematical Analysis and Applications, 2015, Volume 426, Number 2, Page 855
[12]
Daniela De Silva and David Jerison
Communications on Pure and Applied Mathematics, 2011, Volume 64, Number 4, Page 538
[13]
Daniela Silva, Fausto Ferrari, and Sandro Salsa
Discrete and Continuous Dynamical Systems - Series S, 2014, Volume 7, Number 4, Page 673
[14]
J. Ederson M. Braga and Diego R. Moreira
Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 2014, Volume 31, Number 4, Page 823
[15]
D. De Silva and J.M. Roquejoffre
Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 2012, Volume 29, Number 3, Page 335
[16]
X. Cabré and J. Terra
Communications in Partial Differential Equations, 2010, Volume 35, Number 11, Page 1923

Comments (0)

Please log in or register to comment.
Log in