AFRICA MATHEMATICS ANNALS

Partial regularity for Dirichlet - energy minimizing maps between Metric spaces

Moussa KOUROUMA
UFR Mathématiques - Informatique Université de Cocody,
22 BP 582 Abidjan 22, Côte d'Ivoire

Mathematics Subject Classification: (MSC 2000) 58C06, 58C07, 58C35, 49Q20
Key words : Dirichlet form, Ball doubling measure, Dirichlet - energy, Energy minimizing map, Metric space, Regularity

Abstract:

Let (,ρ) and (,d) be two metric spaces such that (,d) is a complete length space with Alexandrov curvature bounded above, and (,ρ) is quasi homogeneous and admits a ball doubling measure μ, and a Dirichlet form b having both some additionnal properties. We prove that any mapping from into , which minimizes locally the Dirichlet - energy defined by μ, is α- Hölder - continuous outside a subset of of Hausdorff - codimension ≥2b, for any .