Seminar talk, 11 March 2009: Difference between revisions

From Geometry of Differential Equations
Jump to navigation Jump to search
New page: Докладчик: Д.Туницкий Тема: О линеаризации систем уравнении Монжа-Ампера Аннотация: Доклад посвящен ...
 
 
(3 intermediate revisions by the same user not shown)
Line 1: Line 1:
Докладчик: Д.Туницкий
Speaker: [[Dmitry Tunitsky]]


Тема: О линеаризации систем уравнении Монжа-Ампера
Title: On the linearization of Monge-Ampère equations




Аннотация:
Abstract:


Доклад посвящен дифференциально-геометрическим структурам,
The talk is devoted to the differential-geometric structures associated to the systems of Monge-Ampère equations on manifolds and their applications to the linearization of these equations. The systems of Monge-Ampère equations that locally equivalent to triangle and semitriangle systems, to systems linear in derivatives (semilinear) with constant coefficients, and to system in total differentials are considered.  Effectively checkable conditions that a given Monge-Ampère system belongs to one of the above types are proved. As consequences, local conditions that a Monge-Ampère system reduces to one equation of second or first order are obtained.
ассоциированным с системами уравнений Монжа-Ампера на
многообразиях, и их применению к линеаризации этих уравнений.
Рассматриваются системы уравнений Монжа-Ампера локально
эквивалентные треугольным и полутреугольным системам, системам
линейным относительно производных (полулинейным), имеющим
постоянные коэффициенты, а также системы в полных дифференциалах.
Доказаны эффективно проверяемые признаки, позволяющие определить,
когда данная система уравнений Монжа-Ампера принадлежит
указанным типам. В качестве следствий получены условия локальной
сводимости системы Монжа-Ампера к одному уравнению второго и
первого порядка.


[[Category: Seminar|Seminar talk 2009-03-11]]
[[Category: Seminar|Seminar talk 7990-96-88]]
[[Category: Seminar abstract|Seminar talk 2009-03-11]]
[[Category: Seminar abstracts|Seminar talk 7990-96-88]]

Latest revision as of 22:09, 17 September 2009

Speaker: Dmitry Tunitsky

Title: On the linearization of Monge-Ampère equations


Abstract:

The talk is devoted to the differential-geometric structures associated to the systems of Monge-Ampère equations on manifolds and their applications to the linearization of these equations. The systems of Monge-Ampère equations that locally equivalent to triangle and semitriangle systems, to systems linear in derivatives (semilinear) with constant coefficients, and to system in total differentials are considered. Effectively checkable conditions that a given Monge-Ampère system belongs to one of the above types are proved. As consequences, local conditions that a Monge-Ampère system reduces to one equation of second or first order are obtained.

Retrieved from "https://gdeq.org/index.php?title=Seminar_talk,_11_March_2009&oldid=372"