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

Luca Capogna, Nicola Garofalo

Type: Article

Publication Date: 2003-03-31

Citations: 58

DOI: https://doi.org/10.1007/s100970200043

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.

Locations

Journal of the European Mathematical Society - View - PDF

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