A Note on the Engulfing Property and the R ^1+α -regularity of Convex Functions in Carnot Groups

Authors

Luca Capogna, University of ArkansasFollow
Diego Maldonado, University of Kansas

Document Type

Article

Publication Date

11-1-2006

Publication Title

Proceedings of the American Mathematical Society

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.

Keywords

Carnot groups, Convexity, Monge-Ampére equation

Volume

134

Issue

11

First Page

3191

Last Page

3199

DOI

10.1090/S0002-9939-06-08359-6

ISSN

00029939

Rights

© 2006 American Mathematical Society.

Comments

Archived as published.

Recommended Citation

Capogna, Luca and Maldonado, Diego, "A Note on the Engulfing Property and the R ^1+α -regularity of Convex Functions in Carnot Groups" (2006). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/145