Regularity of nonlinear flows on noncompact Riemannian manifolds: Differential geometry versus stochastic geometry or what kind of variations is natural?

• Date: 2006
• Main Authors: Antoniouk, A. Val., Antoniouk, A. Vict., Антонюк, О. Вал., Антонюк, О. Вік.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3511
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

It is shown that the geometrically correct investigation of regularity of nonlinear differential flows on manifolds and related parabolic equations requires the introduction of a new type of variations with respect to the initial data. These variations are defined via a certain generalization of a c...