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Classification of Monge-Ampère equations with two variables

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Kruglikov B.

Banach Center Publications

1999

tom 50

nr 1

179-194

This paper deals with the classification of hyperbolic Monge-Ampère equations on a two-dimensional manifold. We solve the local equivalence problem with respect to the contact transformation group assuming that the equation is of general position nondegenerate type. As an application we formulate a new method of finding symmetries. This together with previous author's results allows to state the solution of the classical S. Lie equivalence problem for the Monge-Ampère equations.

The gap phenomenon in the dimension study of finite type systems

100%

Kruglikov B.

Open Mathematics

2012

tom 10

nr 5

1605-1618

Several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the symmetries of geometric structures and differential equations. A general result clarifying this effect in the case when the structure is associated to a vector distribution, is proposed.

Ograniczanie wyników

1 Banach Center Publications

1 Open Mathematics

2 Kruglikov B.

1 2012

1 1999

Wyniki wyszukiwania

Classification of Monge-Ampère equations with two variables

The gap phenomenon in the dimension study of finite type systems