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

Capogna, Luca, and Garofalo, Nicola. "Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type." Journal of the European Mathematical Society 005.1 (2003): 1-40. <http://eudml.org/doc/277621>.

@article{Capogna2003,
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.},
author = {Capogna, Luca, Garofalo, Nicola},
journal = {Journal of the European Mathematical Society},
keywords = {Carnot groups; calculus of variations; minimizer; regularity; Carnot groups; calculus of variations; minimizers; regularity},
language = {eng},
number = {1},
pages = {1-40},
publisher = {European Mathematical Society Publishing House},
title = {Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type},
url = {http://eudml.org/doc/277621},
volume = {005},
year = {2003},
}

TY - JOUR
AU - Capogna, Luca
AU - Garofalo, Nicola
TI - Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type
JO - Journal of the European Mathematical Society
PY - 2003
PB - European Mathematical Society Publishing House
VL - 005
IS - 1
SP - 1
EP - 40
AB - 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.
LA - eng
KW - Carnot groups; calculus of variations; minimizer; regularity; Carnot groups; calculus of variations; minimizers; regularity
UR - http://eudml.org/doc/277621
ER -