Smoothness of harmonic maps for hypoelliptic diffusions

• 成果类型: Article
• 署名作者: Picard, J
• 署名单位: Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1019160255
• 发表日期: 2000
• 页码: 643-666
• 关键词: martingales; probability; REGULARITY; MANIFOLDS; convexity; inequalities

摘要

Harmonic maps are viewed as maps sending a fixed diffusion to manifold-valued martingales. Under a convexity condition, we prove that the continuity of real-valued harmonic functions implies the continuity of harmonic maps. Then we prove with a probabilistic method that continuous harmonic maps are smooth under Hormander's condition; the proof relies on the study of martingales with values in the tangent bundle.