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

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

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...

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Main Authors: Antoniouk, A.Val, Antoniouk, A.Vict.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2004
Series:Український математичний вісник
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/124626
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spelling irk-123456789-1246262017-10-01T03:03:15Z Nonlinear calculus of variations for differential flows on manifolds: geometrically correct introduction of covariant and stochastic variations Antoniouk, A.Val Antoniouk, A.Vict. 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 geometrically rigorous revision of definition of the high order variation with respect to the initial data and parameters. The main attention is devoted to the study of influence of the geometry and nonlinearities of coefficients on the regularity properties. To reach this aim we use the nonlinear symmetries of high order differential calculus and study a set of corresponding nonlinear estimates on variations. The arising conditions on regularity generalize the Krylov-Rosovskii-Pardoux conditions from linear space to the manifold setting. They also lead to the smooth and smoothing properties of associated Feller semigroups. 2004 Article 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. 1810-3200 2000 MSC. 35K05, 47J20, 53B21, 58J35, 60H07, 60H10, 60H30 http://dspace.nbuv.gov.ua/handle/123456789/124626 en Український математичний вісник Інститут прикладної математики і механіки НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description 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 geometrically rigorous revision of definition of the high order variation with respect to the initial data and parameters. The main attention is devoted to the study of influence of the geometry and nonlinearities of coefficients on the regularity properties. To reach this aim we use the nonlinear symmetries of high order differential calculus and study a set of corresponding nonlinear estimates on variations. The arising conditions on regularity generalize the Krylov-Rosovskii-Pardoux conditions from linear space to the manifold setting. They also lead to the smooth and smoothing properties of associated Feller semigroups.
format Article
author Antoniouk, A.Val
Antoniouk, A.Vict.
spellingShingle Antoniouk, A.Val
Antoniouk, A.Vict.
Nonlinear calculus of variations for differential flows on manifolds: geometrically correct introduction of covariant and stochastic variations
Український математичний вісник
author_facet Antoniouk, A.Val
Antoniouk, A.Vict.
author_sort Antoniouk, A.Val
title Nonlinear calculus of variations for differential flows on manifolds: geometrically correct introduction of covariant and stochastic variations
title_short Nonlinear calculus of variations for differential flows on manifolds: geometrically correct introduction of covariant and stochastic variations
title_full Nonlinear calculus of variations for differential flows on manifolds: geometrically correct introduction of covariant and stochastic variations
title_fullStr Nonlinear calculus of variations for differential flows on manifolds: geometrically correct introduction of covariant and stochastic variations
title_full_unstemmed Nonlinear calculus of variations for differential flows on manifolds: geometrically correct introduction of covariant and stochastic variations
title_sort nonlinear calculus of variations for differential flows on manifolds: geometrically correct introduction of covariant and stochastic variations
publisher Інститут прикладної математики і механіки НАН України
publishDate 2004
url http://dspace.nbuv.gov.ua/handle/123456789/124626
citation_txt 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.
series Український математичний вісник
work_keys_str_mv AT antonioukaval nonlinearcalculusofvariationsfordifferentialflowsonmanifoldsgeometricallycorrectintroductionofcovariantandstochasticvariations
AT antonioukavict nonlinearcalculusofvariationsfordifferentialflowsonmanifoldsgeometricallycorrectintroductionofcovariantandstochasticvariations
first_indexed 2023-10-18T20:46:47Z
last_indexed 2023-10-18T20:46:47Z
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