Proceedings of the American Mathematical Society

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

Author(s): Luca Capogna; Diego Maldonado
Journal: Proc. Amer. Math. Soc. 134 (2006), 3191-3199.
MSC (2000): Primary 35Hxx, 52A30
Posted: May 9, 2006
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35Hxx, 52A30

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: 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
Posted: 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
Copyright of article: Copyright 2006, American Mathematical Society

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