An Aleksandrov type estimate for ${\alpha }$-convex functions
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- by Cristian E. Gutiérrez and Federico Tournier PDF
- Proc. Amer. Math. Soc. 138 (2010), 2001-2014 Request permission
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.References
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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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2001-2014
- MSC (2010): Primary 35-XX
- DOI: https://doi.org/10.1090/S0002-9939-10-10255-X
- MathSciNet review: 2596036