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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

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Volume 2009, Issue 635


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


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.

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