Regularity of Minimizers of the Calculus of Variations in Carnot Groups via Hypoellipticity of Systems of Hörmander Type

Authors

Luca Capogna, University of ArkansasFollow
Nicola Garofalo, Johns Hopkins University

Document Type

Article

Publication Date

1-1-2003

Publication Title

Journal of the European Mathematical Society

Abstract

We prove the hypoellipticity for systems of Hörmander type with constant coefficients in Carnot groups of step 2. This result is used to implement blow-up methods and prove partial regularity for local minimizers of non-convex functionals, and for solutions of non-linear systems which appear in the study of non-isotropic metric structures with scalings. We also establish estimates of the Hausdorff dimension of the singular set.

Volume

5

Issue

1

First Page

1

Last Page

40

DOI

10.1007/s100970200043

ISSN

14359855

Comments

Archived as published. Open access paper.

Recommended Citation

Capogna, Luca and Garofalo, Nicola, "Regularity of Minimizers of the Calculus of Variations in Carnot Groups via Hypoellipticity of Systems of Hörmander Type" (2003). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/147