On the backgrounds of the theory of m-Hessian equations

Nina Ivochkina; Nadezda Filimonenkova

doi:10.3934/cpaa.2013.12.1687

Article Contents

2013, Volume 12, Issue 4: 1687-1703. Doi: 10.3934/cpaa.2013.12.1687

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On the backgrounds of the theory of m-Hessian equations

Nina Ivochkina^1, and
Nadezda Filimonenkova^1,

1.
Saint-Petersburg State University of Architecture and Civil Engineering, 2-nd Krasnoarmeiskaya St. 4, 190005 St. Petersburg

Received: July 2011

Revised: April 2012

Published: July 2013

Abstract / Introduction Related Papers Cited by

Abstract

The paper presents some pieces from algebra, theory of function and differential geometry, which have emerged in frames of the modern theory of fully nonlinear second order partial differential equations and revealed their interdependence. It also contains a survey of recent results on solvability of the Dirichlet problem for m-Hessian equations, which actually brought out this development.

Keywords:

$m$-Hessian equations,
$m$-curvatures.

Mathematics Subject Classification: 35J65.

Citation:

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