[Authos]
 Ivochkina, N. M.; Filimonenkova, N. V.

[Title]
 A variational approach to the theory of m-Hessian operators

[AMS Subj-class]
 35J60 Nonlinear elliptic equations
 35J20 Variational methods for second-order elliptic equations

[Abstract]
 The paper presents a survey of the properties of the basic functionals
 related to the m-Hessian operators. The study of the first two is subject
 of works by N. S. Trudinger and Sh.-J. Wang on Hessian measures.
 The purpose of this development is to create the theorem of embedding type
 in cones of admissible functions for m-Hessian operators. The third
 functional was introduced in the paper of 90s by N. M. Ivochkina where
 variational description of the cone of m-admissible functions was presented.
 We keep to both directions, exploring the relationship of known facts and
 deduce some new results.

[Keywords]
 m-Hessian operator, cone of m-admissible functions, variational description

[Comments]
 LaTeX, Russian, 18 pp.
 The paper is accepted for publishing by "Proceedings of St. Petersburg
 Mathematical Society" in 2013.

[Contact e-mail]
 nf33@yandex.ru