JournalsjemsVol. 5 , No. 1DOI 10.1007/s100970200043

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 States
  • Nicola Garofalo

    Università di Padova, Italy
Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type cover

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.