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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An Aleksandrov type estimate for $ {\alpha}$-convex functions


Authors: Cristian E. Gutiérrez and Federico Tournier
Journal: Proc. Amer. Math. Soc. 138 (2010), 2001-2014
MSC (2010): Primary 35-XX
Published electronically: February 16, 2010
MathSciNet review: 2596036
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Abstract: In the context of $ {\alpha}$-convexity, using an operator similar to the Monge-Ampère operator based on the notion of normal mapping, we estimate the difference between a function $ u$ and the solution of the homogeneous problem $ U$ in terms of the measure of the normal mapping of $ u$ and a power of the distance to the boundary.


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Additional Information

Cristian E. Gutiérrez
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Email: gutierre@temple.edu

Federico Tournier
Affiliation: Instituto Argentino de Matemática, CONICET, Buenos Aires, Argentina
Email: fedeleti@aim.com

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10255-X
PII: S 0002-9939(10)10255-X
Received by editor(s): October 27, 2008
Published electronically: February 16, 2010
Additional Notes: The first author was partially supported by NSF grant DMS–0610374.
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.