On algebraic and geometric conditions in the theory of Hessian equations

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.

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Correspondence to N. M. Ivochkina.

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To Professor Andrzej Granas

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Ivochkina, N.M., Filimonenkova, N.V. On algebraic and geometric conditions in the theory of Hessian equations. J. Fixed Point Theory Appl. 16, 11–25 (2014). https://doi.org/10.1007/s11784-015-0217-4

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MathemMathematics Subject Classification

  • Primary 35K61
  • Secondary 15B48

Keywords

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