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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 2012, Issue 667


Hessian inequalities and the fractional Laplacian

Fausto Ferrari / Bruno Franchi / Igor E. Verbitsky
Published Online: 2011-07-14 | DOI: https://doi.org/10.1515/CRELLE.2011.116


We study relations between the k-Hessian energy , and the fractional Sobolev energy , where Fk (k = 1, . . . , n) is the k-Hessian operator on ℝn, and u is a k-convex function vanishing at ∞. We prove that there is a constant C > 0 such that C−1Ek[u] ≦ ℰk[u] ≦ CEk[u], where the lower estimate is obtained under some additional assumptions on u. In general, we show that there exists a function ũ such that c−1 ≦ |u/ũ| ≦ c, and C−1Ek[ũ] ≦ ℰk[u] ≦ CEk[ũ], where c, C are positive constants depending only on k and n.

About the article

Received: 2010-05-05

Revised: 2010-10-06

Published Online: 2011-07-14

Published in Print: 2012-06-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2012, Issue 667, Pages 133–148, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2011.116.

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