Email this article On New Structures in the Theory of Fully Nonlinear Equations
- Authors: Ivochkina N.M.1, Filimonenkova N.V.2,3
-
Affiliations:
- St. Petersburg State University
- St. Petersburg State University of Architecture and Civil Engineering
- Peter the Great St. Petersburg Polytechnic University
- Issue: Vol 233, No 4 (2018)
- Pages: 480-494
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241571
- DOI: https://doi.org/10.1007/s10958-018-3939-1
- ID: 241571
Cite item
Open Access
Access granted
Subscription Access
Abstract
We describe the current state of the theory of equations with m-Hessian stationary and evolution operators. It is quite important that new algebraic and geometric notions appear in this theory. In the present work, a list of those notions is provided. Among them, the notion of m-positivity of matrices is quite important; we provide a proof of an analog of Sylvester’s criterion for such matrices. From this criterion, we easily obtain necessary and sufficient conditions for existence of classical solutions of the first initial boundary-value problem for m-Hessian evolution equations. The asymptotic behavior of m-Hessian evolutions in a semibounded cylinder is considered as well.
About the authors
N. M. Ivochkina
St. Petersburg State University
Author for correspondence.
Email: ninaiv@NI1570.spb.edu
Russian Federation, Saint Petersburg
N. V. Filimonenkova
St. Petersburg State University of Architecture and Civil Engineering; Peter the Great St. Petersburg Polytechnic University
Email: ninaiv@NI1570.spb.edu
Russian Federation, Saint Petersburg; Saint Petersburg
Supplementary files
