Contents > Past issues > Volume 3

**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
.