Finding solutions of parabolic Monge-Ampere equations by using the geometry of sections of the contact distribution

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Publikace nespadá pod Pedagogickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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ALEKSEEVSKIY Dmitry MANNO Gianni PUGLIESE Fabrizio ALONCO-BLANCO Ricardo

Rok publikování 2014
Druh Článek v odborném periodiku
Časopis / Zdroj Differential Geometry and its Applications
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://doi.org/10.1016/j.difgeo.2013.10.015
Doi http://dx.doi.org/10.1016/j.difgeo.2013.10.015
Obor Obecná matematika
Klíčová slova Parabolic Monge Ampere equations; Characteristic distribution; Construction of solutions
Popis In a series of papers we have described normal forms of parabolic Monge–Ampere equations (PMAEs) by means of their characteristic distribution. In particular, PMAEs with two independent variables are associated with Lagrangian (or Legendrian) subdistributions of the contact distribution of a 5-dimensional contact manifold. The geometry of sections of the contact distribution allowed us to get the aforementioned normal forms. In the present work, for a distinguished class of PMAEs, we will construct 3-parametric families of solutions starting from particular sections of the characteristic distribution. We will illustrate the method by several concrete computations. Moreover, we will see, for some linear PMAEs, how to construct a recursive process for obtaining new solutions. At the end, after showing that some classical equations on affine connected 3-dimensional manifolds are PMAEs, we will apply the integration method to some particular examples.
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