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Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type

Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type

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Publisher
Springer Journals
Copyright
Copyright © 2003 by Springer-Verlag Berlin Heidelberg & EMS
Subject
Mathematics; Mathematics, general
ISSN
1435-9855
DOI
10.1007/s100970200043
Publisher site
See Article on Publisher Site

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.

Journal

Journal of the European Mathematical SocietySpringer Journals

Published: Mar 1, 2003

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