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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 2013, Issue 680


Convexity estimates for level sets of quasiconcave solutions to fully nonlinear elliptic equations

Pengfei Guan / Xu Lu
  • Wuhan Institute of Physics and Mathematics, The Chinese Academy of Science, Wuhan, 430071, HuBei Province, P.R. China
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Published Online: 2012-04-03 | DOI: https://doi.org/10.1515/crelle.2012.038


We establish a global geometric lower bound for the second fundamental form of the level surfaces of solutions to F(D2u, Du, u, x) = 0 in convex ring domains, in terms of boundary geometry and the structure of the elliptic operator F. We also prove a microscopic constant rank theorem, under a general structural condition introduced by Bianchini–Longinetti–Salani in 2009.

About the article

Received: 2010-10-28

Revised: 2011-09-24

Published Online: 2012-04-03

Published in Print: 2013-06-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2013, Issue 680, Pages 41–67, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle.2012.038.

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