Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type
Luca Capogna
University of Arkansas, Fayetteville, United StatesNicola Garofalo
Università di Padova, Italy
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.
Cite this article
Luca Capogna, Nicola Garofalo, Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type. J. Eur. Math. Soc. 5 (2003), no. 1, pp. 1–40
DOI 10.1007/S100970200043