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On algebraic and geometric conditions in the theory of Hessian equations

  • N. M. IvochkinaEmail author
  • N. V. Filimonenkova
Article

Abstract

The paper is a kind of survey which contains a description of new algebraic and geometric structures together with fragments of a technique developed in the theory of Hessian equations. Our principal concern here is the m-Hessian evolutionary equations, and we formulate some existence and nonexistence theorems of solutions to the first initial boundary value problems in C 2(Q̄ T ) for such equations.

MathemMathematics Subject Classification

Primary 35K61 Secondary 15B48 

Keywords

m-Hessian equation m-positive matrix m-admissible function p-curvature boundary barrier m-convex hypersurface 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Faculty of Mathematics and MechanicsSt.Petersburg State UniversitySt.PetersburgRussia
  2. 2.St.Petersburg State University of Architecture and Civil EngineeringSt.PetersburgRussia
  3. 3.St.Petersburg Polytechnic UniversitySt.PetersburgRussia

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