Geodesic
Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type
Journal of the European Mathematical Society, Tome 5 (2003) no. 1, pp. 1-40
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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.
DOI : 10.1007/s100970200043
Classification : 49-XX, 35-XX, 46-XX, 00-XX
Keywords: 
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     author = {Luca Capogna and Nicola Garofalo},
     title = {Regularity of minimizers of the calculus of variations in {Carnot} groups via hypoellipticity of systems of {H\"ormander} type},
     journal = {Journal of the European Mathematical Society},
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     year = {2003},
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Luca Capogna; Nicola Garofalo. Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type. Journal of the European Mathematical Society, Tome 5 (2003) no. 1, pp. 1-40. doi: 10.1007/s100970200043

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