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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on the engulfing property and the $\Gamma ^{1+ \alpha }$-regularity of convex functions in Carnot groups
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by Luca Capogna and Diego Maldonado PDF
Proc. Amer. Math. Soc. 134 (2006), 3191-3199 Request permission

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.
References
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Additional Information
  • Luca Capogna
  • Affiliation: Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701
  • MR Author ID: 336615
  • 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
  • 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
  • © Copyright 2006 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 3191-3199
  • MSC (2000): Primary 35Hxx, 52A30
  • DOI: https://doi.org/10.1090/S0002-9939-06-08359-6
  • MathSciNet review: 2231902