Nonlinear calculus of variations for differential flows on manifolds: geometrically correct introduction of covariant and stochastic variations

• Published in: Український математичний вісник
• Date: 2004
• Main Authors: Antoniouk, A.Val, Antoniouk, A.Vict.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2004
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/124626
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Nonlinear calculus of variations for differential flows on manifolds: geometrically correct introduction of covariant and stochastic variations / A.Val. Antoniouk, A.Vict. Antoniouk // Український математичний вісник. — 2004. — Т. 1, № 4. — С. 449-484. — Бібліогр.: 23 назв. — англ.

We consider flows, generated by nonlinear differential equations on manifold that could also contain random terms and correspond to the second order parabolic equations. We demonstrate that the rigorous statement of the regularity problems for differential flows on noncompact manifolds requires the...