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

Luca Capogna | Zendy; Nicola Garofalo | Zendy

Open Access

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

Author(s) -

Luca Capogna,

Nicola Garofalo

Publication year - 2003

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.1007/s100970200043

Subject(s) - mathematics , carnot cycle , type (biology) , pure mathematics , mathematical analysis , regular polygon , metric (unit) , isotropy , geometry , ecology , operations management , physics , quantum mechanics , economics , biology , thermodynamics

. 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.

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