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

 

A note on the engulfing property and the $ \Gamma^{1+ \alpha}$-regularity of convex functions in Carnot groups


Authors: Luca Capogna and Diego Maldonado
Journal: Proc. Amer. Math. Soc. 134 (2006), 3191-3199
MSC (2000): Primary 35Hxx, 52A30
Published electronically: May 9, 2006
MathSciNet review: 2231902
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Abstract: We study the engulfing property for convex functions in Carnot groups. As an application we show that the horizontal gradient of functions with this property is Hölder continuous.


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Additional Information

Luca Capogna
Affiliation: Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701
Email: lcapogna@comp.uark.edu

Diego Maldonado
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Address at time of publication: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: maldonado@math.ku.edu, maldona@math.umd.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08359-6
PII: S 0002-9939(06)08359-6
Keywords: Carnot groups, convexity, Monge-Amp\'ere equation
Received by editor(s): May 9, 2005
Published electronically: May 9, 2006
Additional Notes: The first author was partially supported by the NSF Faculty Early Career Award DMS 0134318
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2006 American Mathematical Society